user3007: What is the longest move sequence that ends with checkmate and every move is a check by both players?

user10380: The question asked in the title is different from the question asked in the body.
If it is required that every best option is check, but it is allowed for the players to have non-checking alternatives, then I offer the following. Every best option for White, i.e. every White move which enables White to mate in time against any Black defence (not just checks), is check. White has other moves available which are not check, but they fail to mate in time. Every best option for Black, i.e. every Black move which gives White only one move-sequence which enables White to mate in time, is check. Black has other moves available which are not check, but they either enable White to mate sooner, or give White a choice.
[Title "J. Rotenberg, Problemiste 2012, 1st pr.; PDB 1298074. #11"]
[fen "3Bn1N1/qrrpbppn/1Pppp1p1/2QR1Nk1/3PKR2/8/b2p2P1/8 w KQkq - 0 1"]
[StartFlipped "0"]

1.Nfxe7+ exd5+ 2.Nxd5+ Nef6+ 3.Ndxf6+ d5+ 4.Nxd5+ Nf6+ 5.Ndxf6+ d5+ 6.Nxd5+ Re7+ 7.Ndxe7+ Bd5+ 8.Nxd5+ Re7+ 9.Ndxe7+ f5+ 10.Nxf5+ Qe7+ 11.Nfxe7#


Here's Rotenberg's original problem of which the above is a correction.
[Title "J. Rotenberg, Europe Echecs 1978; Morse, 1st ed., 835; PDB 1298046. #11"]
[fen "3Bn1N1/qrrpbppn/1Pppp1p1/2QR1Nk1/3PKR2/1b6/6P1/8 w KQkq - 0 1"]
[StartFlipped "0"]

1.Nfxe7+ exd5+ (1... cxd5+ 2.Nxd5+ Nef6+ 3.Ndxf6+ d5+ 4.Nxd5+ Nf6+ 5.Ndxf6+ d5+ 6.Nxd5+ Re7+ 7.Ndxe7+ f5+ 8.Nxf5+ Re7 9.Qxe7+ Qxe7 10.Bxe7+ ~ 11.Rh4#) (1... f5+ 2.Rdxf5+ exf5+ 3.Rxf5+ Kg4 4.Rf4+ ~ 5. Qc3+ Kh2 6.Rh4+) (1...e5 2.Rxe5+ dxe5 3.Qxe5+ f5+ 4.Rxf5+) 2.Nxd5+ Nef6+ (2... f6 3.Ndxf6+ {and mate in 9}) 3.Ndxf6+ d5+ 4.Nxd5+ Nf6+ 5.dNxf6+ d5+ 6.Nxd5+ Re7+ 7.Ndxe7+ Bd5+ 8.Nxd5+ Re7+ 9.Ndxe7+ f5+ 10.Nxf5+ Qe7+ 11.Ndxe7#

The sideline after 1... cxd5+ is not best for Black because it gives White the duals 9.Qxe7+ Qxe7 10.Bxe7+ and 9.Bxe7+ Qxe7 10.Qxe7+. And it also gives Black non-checking options which force White to take the full 11 moves.
The sideline after 2... f6 is not best for Black because it enables White to mate in 9.
The above observation, and the choice of sidelines, are by Morse.
Unfortunately this problem is cooked. PDB notes a shorter win in 9.

If it is required that every White move and every Black move is forced, I don't know the answer.

user15543: Rosie F’s answer is a wonderful one.
However, if you want it to be forced in terms of returning a check with a check, and having to make that move by the laws of chess, I have a different answer. The positions are legal and are checkmating problems as required.
The record with each player having multiple legal moves is 22 ply.
[Title "Alexey Khanyan, Tim Krabbe’s Website #267 2008, Mate in 11"]
[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
If you want it so each player has only one legal move, the known record is 15 ply.
[Title "shoopi, www.chess.com 6/11/2013, Mate In 8"]
[FEN "rk1KB3/b1q1QQQR/bnqQ1q2/1Rq1Q1q1/2q1rQ1q/6B1/6QQ/8 w - - 0 1"]

1. Qxc7+ Qxc7+ 2. Qxc7+ Qxc7+ 3. Qxc7+ Qxc7+ 4. Bxc7+ Kb7+ 5. Bb8+ Qxe7+ 6. Qxe7+ Qxe7+ 7. Qxe7+ Qxe7+ 8. Rxe7#

Source: The Die Schwalbe Chess Problem Database
Additional Source: The original page!

user2800: I'm not aware of any resources documenting the specific situation you're asking about. The closest available is probably this page from Tim Krabbé's chess records which documents the longest known series of mutual checks, but not ending in checkmate.
One of the puzzles from the page could end in checkmate via 14.. Qb7# instead of 14...Bxb7+, so this would be an example of a checkmate after 27 consecutive checks. This series of checks could be considered "forced" by the objective of the puzzle.
[Title "G. Leathem, Fairy Chess Review, 1938, 28 Consecutive Checks"]
[FEN "K2kn2r/NP1P1PPP/1PPPnNq1/1Rr1Bb1Q/4R3/8/8/8 w - - 0 1"]

1. c7+ N8xc7+ 2. bxc7+ Nxc7+ 3. dxc7+ Ke7+ 4. g8=N+ Rxg8+ 5. hxg8=N+ Qxg8+ 6. f8=Q+ Qxf8+ 7. Qe8+ Qxe8+ 8. d8=Q+ Qxd8+ 9. c8=N+ Rxc8+ 10. bxc8=N+ Qxc8+ 11. Bb8+ Bxe4+ 12. Nd5+ Bxd5+ 13. Nc6+ Bxc6+ 14. Rb7+ Bxb7 (14...Qxb7#)


3007: <p>What is the longest move sequence that ends with checkmate and every move is a check by both players?</p>
 10380: <p>The question asked in the title is different from the question asked in the body.</p>

<p>If it is required that every best option is check, but it is allowed for the players to have non-checking alternatives, then I offer the following. Every best option for White, i.e. every White move which enables White to mate in time against any Black defence (not just checks), is check. White has other moves available which are not check, but they fail to mate in time. Every best option for Black, i.e. every Black move which gives White only one move-sequence which enables White to mate in time, is check. Black has other moves available which are not check, but they either enable White to mate sooner, or give White a choice.</p>

<pre><code>[Title "J. Rotenberg, Problemiste 2012, 1st pr.; PDB 1298074. #11"]
[fen "3Bn1N1/qrrpbppn/1Pppp1p1/2QR1Nk1/3PKR2/8/b2p2P1/8 w KQkq - 0 1"]
[StartFlipped "0"]

1.Nfxe7+ exd5+ 2.Nxd5+ Nef6+ 3.Ndxf6+ d5+ 4.Nxd5+ Nf6+ 5.Ndxf6+ d5+ 6.Nxd5+ Re7+ 7.Ndxe7+ Bd5+ 8.Nxd5+ Re7+ 9.Ndxe7+ f5+ 10.Nxf5+ Qe7+ 11.Nfxe7#
</code></pre>

<hr>

<p>Here's Rotenberg's original problem of which the above is a correction.</p>

<pre><code>[Title "J. Rotenberg, Europe Echecs 1978; Morse, 1st ed., 835; PDB 1298046. #11"]
[fen "3Bn1N1/qrrpbppn/1Pppp1p1/2QR1Nk1/3PKR2/1b6/6P1/8 w KQkq - 0 1"]
[StartFlipped "0"]

1.Nfxe7+ exd5+ (1... cxd5+ 2.Nxd5+ Nef6+ 3.Ndxf6+ d5+ 4.Nxd5+ Nf6+ 5.Ndxf6+ d5+ 6.Nxd5+ Re7+ 7.Ndxe7+ f5+ 8.Nxf5+ Re7 9.Qxe7+ Qxe7 10.Bxe7+ ~ 11.Rh4#) (1... f5+ 2.Rdxf5+ exf5+ 3.Rxf5+ Kg4 4.Rf4+ ~ 5. Qc3+ Kh2 6.Rh4+) (1...e5 2.Rxe5+ dxe5 3.Qxe5+ f5+ 4.Rxf5+) 2.Nxd5+ Nef6+ (2... f6 3.Ndxf6+ {and mate in 9}) 3.Ndxf6+ d5+ 4.Nxd5+ Nf6+ 5.dNxf6+ d5+ 6.Nxd5+ Re7+ 7.Ndxe7+ Bd5+ 8.Nxd5+ Re7+ 9.Ndxe7+ f5+ 10.Nxf5+ Qe7+ 11.Ndxe7#
</code></pre>

<p>The sideline after 1... cxd5+ is not best for Black because it gives White the duals 9.Qxe7+ Qxe7 10.Bxe7+ and 9.Bxe7+ Qxe7 10.Qxe7+. And it also gives Black non-checking options which force White to take the full 11 moves.</p>

<p>The sideline after 2... f6 is not best for Black because it enables White to mate in 9.</p>

<p>The above observation, and the choice of sidelines, are by Morse.</p>

<p>Unfortunately this problem is cooked. PDB notes a shorter win in 9.</p>

<hr>

<p>If it is required that every White move and every Black move is forced, I don't know the answer.</p>
 15543: <p>Rosie F’s answer is a wonderful one.</p>
<p>However, if you want it to be forced in terms of returning a check with a check, and having to make that move by the laws of chess, I have a different answer. The positions are legal and are checkmating problems as required.</p>
<p>The record with each player having multiple legal moves is 22 ply.</p>
<pre><code>[Title &quot;Alexey Khanyan, Tim Krabbe’s Website #267 2008, Mate in 11&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>If you want it so each player has only one legal move, the known record is 15 ply.</p>
<pre><code>[Title &quot;shoopi, www.chess.com 6/11/2013, Mate In 8&quot;]
[FEN &quot;rk1KB3/b1q1QQQR/bnqQ1q2/1Rq1Q1q1/2q1rQ1q/6B1/6QQ/8 w - - 0 1&quot;]

1. Qxc7+ Qxc7+ 2. Qxc7+ Qxc7+ 3. Qxc7+ Qxc7+ 4. Bxc7+ Kb7+ 5. Bb8+ Qxe7+ 6. Qxe7+ Qxe7+ 7. Qxe7+ Qxe7+ 8. Rxe7#
</code></pre>
<p>Source: <a href="https://pdb.dieschwalbe.de/P1374763" rel="nofollow noreferrer">The Die Schwalbe Chess Problem Database</a></p>
<p>Additional Source: <a href="https://www.chess.com/forum/view/more-puzzles/self-solving-puzzles?page=3" rel="nofollow noreferrer">The original page!</a></p>
 2800: <p>I'm not aware of any resources documenting the specific situation you're asking about. The closest available is probably <a href="http://timkr.home.xs4all.nl/chess/check.html" rel="nofollow noreferrer">this page</a> from <a href="http://timkr.home.xs4all.nl/records/records.htm" rel="nofollow noreferrer">Tim Krabbé's chess records</a> which documents the longest known series of mutual checks, but not ending in checkmate.</p>

<p>One of the puzzles from the page could end in checkmate via 14.. Qb7# instead of 14...Bxb7+, so this would be an example of a checkmate after 27 consecutive checks. This series of checks could be considered "forced" by the objective of the puzzle.</p>

<pre><code>[Title "G. Leathem, Fairy Chess Review, 1938, 28 Consecutive Checks"]
[FEN "K2kn2r/NP1P1PPP/1PPPnNq1/1Rr1Bb1Q/4R3/8/8/8 w - - 0 1"]

1. c7+ N8xc7+ 2. bxc7+ Nxc7+ 3. dxc7+ Ke7+ 4. g8=N+ Rxg8+ 5. hxg8=N+ Qxg8+ 6. f8=Q+ Qxf8+ 7. Qe8+ Qxe8+ 8. d8=Q+ Qxd8+ 9. c8=N+ Rxc8+ 10. bxc8=N+ Qxc8+ 11. Bb8+ Bxe4+ 12. Nd5+ Bxd5+ 13. Nc6+ Bxc6+ 14. Rb7+ Bxb7 (14...Qxb7#)
</code></pre>
