user25158: A usual forced mate position is where the winning player can play in a way that ensures checkmate, no matter what (legal) moves the opponent makes (unless the game ends due to a non-play reason, i.e. resignation, draw accepted, time ran out.)
What I'm asking about here is what I'll call a double-forced mate:  A position where checkmate is ensured no matter what (legal) moves either player makes.
With this rule alone we can find a position such as this, where white has only one legal move, resulting in checkmate.  Let's call this type 1.
Type 1:
[FEN "K1k5/1q6/P7/B3N3/8/8/8/8 w - - 0 1"]

1. axb7#

The only option is axb7#. However, this isn't too satisfying as a "double" forced mate, as there was only a single possible move to continue.  We can explore positions that have multiple possibilities, but still ensure checkmate absolutely.
Type 2:
[FEN "k7/2QQQQQQ/KQ1QQQQQ/QQQ1QQQQ/QQQQ1QQQ/QQQQQ1QQ/QQQQQQ1Q/QQQQQQQ1 w - - 0 1"]

White has many legal moves, but every one of them results in an immediate checkmate.  Still, I feel this question isn't quite answered, as in a true double-forced checkmate, both players should play a role. (Also, this position clearly isn't possible from a standard board start. And even if it were, it doesn't seem that it could be achieved without first creating a stalemate.)  Let's finally look to type 3.
Type 3:
The true double-forced mate: A position where checkmate is ensured no matter what (legal) moves either player makes, however there is at least some line where both players make a move. Meaning not every legal ply in the start position is an immediate checkmating move.
Do you know of (or can you find) any such chess positions of (type 3) double-forced mate?  Or can you prove that this is not possible?
Also, share if you have any interesting or more plausible examples of type 1 and 2.

user26346: Rewan Demontay already has a great answer. However, I would also like to add this 'self-solving' chess problem from Tim Krabbé's Chess Diary #267. Here, all moves are forced and will lead to a checkmate. The composer's full name comes from chess problem databases.
[Title "Vilhelm Röpke, Skakbladet 1942, Mate In 6"]
[FEN "K1k5/P1Pp4/1p1P4/8/p7/P2P4/8/8 w - - 0 1"]


1. d4 b5 2. d5 b4 3. axb4 a3 4. b5 a2 5. b6 a1=Q 6. b7#

Although it does not completely satisfy your type 3 requirement that checkmate is not guaranteed in the first ply, I think it is a nice little puzzle that has some similarities with your question.

user25158: Inspired by Thijs van Ede's answer, I've modified the pattern from Chess Diary #267
[FEN "K1k5/P1Pp4/3P4/1P6/1P6/8/5p2/8 w - - 0 1"]

1. b6 f1=B 2. b7# (2. b5 Bg2+ 3. b7+ Bxb7#)

This position features something rather strange.  Still according to the rules, checkmate is ensured no matter what legal moves either player makes.  However, it is not guaranteed which player shall deliver checkmate.  The outcome depends on what piece black promotes to.
In any case, white can just push b6 and b7 to mate before black can respond.  However if white delays with b6 followed by b5, black can save themself and checkmate white by choosing the queen or bishop.  See the example line or try it yourself on lichess.

user15543: Indeed, there are many possible positions in which all mates are forced on the first ply. Since you ask not for that, I shall provide examples with more than one move by both sides.
Here is the known, and overall, length record for both sides having multiple legal moves since you said that a single line "isn't too satisfying."
[Title "Alexey Khanyan, Tim Krabbe's Website Diary Entry #267 2008, Mate In 11 Moves/22 Plies"]
[FEN "4Q2Q/4r3/4n1n1/1bbK1krn/RR1RR1RR/2qn1R1n/4n1nN/Q3Q3 b - - 0 1"]
[startflipped ""]

1... Ng2f4+ 2. Rfxf4+ N2xf4+ 3. Rgxf4+ Nh3xf4+ 4. Rhxf4+ Ndxf4+ 5. Rxf4+ Nhxf4+ 6. Rxf4+ Ngxf4+ 7. Rxf4+ Nxf4+ 8. Rxf4+ Kxf4+ 9. Qee5+ Qxe5+ 10. Qaxe5+ Rgxe5+ 11. Qxe5+ Rxe5+ 12. Qxe5#

Source: Diary Entry #267
Additionally, I know of this simple problem that illustrates it with either player giving mate.
[Title "Eugene B. Cook, The Chess Amateur 1926, Mate In For White And Black"]
[FEN "Bk6/1P6/1P3p2/8/8/2P3p1/6p1/6Kb w - - 0 1"]

Lastly, be sure to check out a funny mutual zugzwang position in this CSE question by the user @Peter, in which both sides are forced to let the other mate them!

25158: <p>A usual forced mate position is where the winning player can play in a way that ensures checkmate, <strong>no matter what (legal) moves the opponent makes</strong> (unless the game ends due to a non-play reason, i.e. resignation, draw accepted, time ran out.)</p>
<p>What I'm asking about here is what I'll call a double-forced mate:  A position where checkmate is ensured no matter what (legal) moves <strong>either</strong> player makes.</p>
<p>With this rule alone we can find a position such as this, where white has only one legal move, resulting in checkmate.  Let's call this type 1.</p>
<h1>Type 1:</h1>
<pre><code>[FEN &quot;K1k5/1q6/P7/B3N3/8/8/8/8 w - - 0 1&quot;]

1. axb7#
</code></pre>
<p>The only option is <code>axb7#</code>. However, this isn't too satisfying as a &quot;double&quot; forced mate, as there was only a single possible move to continue.  We can explore positions that have multiple possibilities, but still ensure checkmate absolutely.</p>
<h1>Type 2:</h1>
<pre><code>[FEN &quot;k7/2QQQQQQ/KQ1QQQQQ/QQQ1QQQQ/QQQQ1QQQ/QQQQQ1QQ/QQQQQQ1Q/QQQQQQQ1 w - - 0 1&quot;]
</code></pre>
<p>White has many legal moves, but every one of them results in an immediate checkmate.  Still, I feel this question isn't quite answered, as in a true double-forced checkmate, both players should play a role. (Also, this position clearly isn't possible from a standard board start. And even if it were, it doesn't seem that it could be achieved without first creating a stalemate.)  Let's finally look to type 3.</p>
<h1>Type 3:</h1>
<p>The <em>true</em> double-forced mate: A position where checkmate is ensured no matter what (legal) moves <strong>either</strong> player makes, however there is at least some line where both players make a move. Meaning not every legal ply in the start position is an immediate checkmating move.</p>
<p>Do you know of (or can you find) any such chess positions of (type 3) double-forced mate?  Or can you prove that this is not possible?</p>
<p>Also, share if you have any interesting or more plausible examples of type 1 and 2.</p>
 26346: <p>Rewan Demontay already has a great answer. However, I would also like to add this 'self-solving' chess problem from Tim Krabbé's <a href="https://timkr.home.xs4all.nl/chess2/diary_14.htm" rel="noreferrer">Chess Diary #267</a>. Here, all moves are forced and will lead to a checkmate. The composer's full name comes from chess <a href="https://www.yacpdb.org/#103072" rel="noreferrer">problem</a> <a href="https://pdb.dieschwalbe.de/P1180283" rel="noreferrer">databases.</a></p>
<pre><code>[Title &quot;Vilhelm Röpke, Skakbladet 1942, Mate In 6&quot;]
[FEN &quot;K1k5/P1Pp4/1p1P4/8/p7/P2P4/8/8 w - - 0 1&quot;]


1. d4 b5 2. d5 b4 3. axb4 a3 4. b5 a2 5. b6 a1=Q 6. b7#
</code></pre>
<p>Although it does not completely satisfy your type 3 requirement that checkmate is not guaranteed in the first ply, I think it is a nice little puzzle that has some similarities with your question.</p>
 25158: <p>Inspired by Thijs van Ede's answer, I've modified the pattern from <a href="https://timkr.home.xs4all.nl/chess2/diary_14.htm" rel="nofollow noreferrer">Chess Diary #267</a></p>
<pre><code>[FEN &quot;K1k5/P1Pp4/3P4/1P6/1P6/8/5p2/8 w - - 0 1&quot;]

1. b6 f1=B 2. b7# (2. b5 Bg2+ 3. b7+ Bxb7#)
</code></pre>
<p>This position features something rather strange.  Still according to the rules, checkmate is ensured no matter what legal moves either player makes.  However, it is not guaranteed <strong>which</strong> player shall deliver checkmate.  The outcome depends on what piece black promotes to.</p>
<p>In any case, white can just push <code>b6</code> and <code>b7</code> to mate before black can respond.  However if white delays with <code>b6</code> followed by <code>b5</code>, black can save themself and checkmate white by choosing the queen or bishop.  See the example line or try it yourself on <a href="https://lichess.org/analysis/K1k5/P1Pp4/3P4/1P6/1P6/8/5p2/8_w_-_-_0_1" rel="nofollow noreferrer">lichess</a>.</p>
 15543: <p>Indeed, there are <a href="https://chess.stackexchange.com/questions/24061/what-is-the-highest-number-of-possible-forced-checkmates-in-a-legal-position">many</a> <a href="https://chess.stackexchange.com/questions/24033/a-position-in-which-checkmate-is-forced-obligatory/24034#24034">possible</a> <a href="https://puzzling.stackexchange.com/questions/30409/highest-number-of-mates/87225#87225">positions</a> in which all mates are forced on the first ply. Since you ask not for that, I shall provide examples with more than one move by both sides.</p>
<p>Here is the known, and overall, length record for both sides having multiple legal moves since you said that a single line &quot;isn't too satisfying.&quot;</p>
<pre><code>[Title &quot;Alexey Khanyan, Tim Krabbe's Website Diary Entry #267 2008, Mate In 11 Moves/22 Plies&quot;]
[FEN &quot;4Q2Q/4r3/4n1n1/1bbK1krn/RR1RR1RR/2qn1R1n/4n1nN/Q3Q3 b - - 0 1&quot;]
[startflipped &quot;&quot;]

1... Ng2f4+ 2. Rfxf4+ N2xf4+ 3. Rgxf4+ Nh3xf4+ 4. Rhxf4+ Ndxf4+ 5. Rxf4+ Nhxf4+ 6. Rxf4+ Ngxf4+ 7. Rxf4+ Nxf4+ 8. Rxf4+ Kxf4+ 9. Qee5+ Qxe5+ 10. Qaxe5+ Rgxe5+ 11. Qxe5+ Rxe5+ 12. Qxe5#
</code></pre>
<p>Source: <a href="https://timkr.home.xs4all.nl/chess2/diary_14.htm" rel="nofollow noreferrer">Diary Entry #267</a></p>
<p>Additionally, I know of <a href="https://pdb.dieschwalbe.de/P1108329" rel="nofollow noreferrer">this</a> simple problem that illustrates it with either player giving mate.</p>
<pre><code>[Title &quot;Eugene B. Cook, The Chess Amateur 1926, Mate In For White And Black&quot;]
[FEN &quot;Bk6/1P6/1P3p2/8/8/2P3p1/6p1/6Kb w - - 0 1&quot;]
</code></pre>
<p>Lastly, be sure to check out a funny mutual zugzwang position in <a href="https://chess.stackexchange.com/questions/9062/full-board-with-full-point-mutual-zugzwang">this</a> CSE question by the user @Peter, in which both sides are forced to let the other mate them!</p>
