user15543: The record for the most mutual checks in a legal position is known. But what is the record for double checks? There is one rule-threefold repetition applies. Four criteria exist-promoted pieces allowed and not along with forced, Black defends, and unforced, Black helps. Below is my research.

[Title "No Promoted Pieces, Unforced-6"]
[FEN "4K3/8/8/3p4/k1p1N3/1p4N1/P5BB/RRQ5 w - - 0 1"]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kxd5 4. Nc3+ Kd6 5. Nf5+ Kc5 6. Na4#


[Title "No Promoted Pieces, Forced-5"]
[FEN "kb1r4/P1p5/1P2P3/6NB/7B/8/8/RRQ4K w - - 0 1"]

1. axb8=Q+ Kxb8 2. bxc7+ Kc8 3. cxd8=Q+ Kxd8 4. Nf7+ Ke8 5. Nd6+ Kf8


[Title "Promoted Pieces, Unforced-9"]
[FEN "K5b1/5p2/4p3/3pR3/k1p1N1N1/1pQ5/P1B5/RR1R1RRR w - - 0 1"]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kd7 4. dxe6+ Ke8 5. exf7+ Kf8 6. fxg8=Q+ Kxg8 7. Nh6+ Kh7 8. Nf6+ Kh8 9. Nf7#


[Title "Promoted Pieces, Forced-8"]
[FEN "K4Bb1/5p2/4p3/3p4/k1p3N1/1pR5/P1B5/RQ1RRRRR w - - 0 1"]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kd7 4. dxe6+ Ke8 5. exf7+ Kxf8 6. fxg8=Q+ Kxg8 7. Nh6+ Kh8 8. Nf7#


Addendum: @Hauke Reddmann commented a known double checking mechanism, but no origin is given. The likely origin of it is a century old problem as @Evargalo proposed a comment.
[Title "Alain Campbell White, Pittsburgh Gazette Times 4/1916, Mate In 12"]
[FEN "2q5/2pp4/3pr3/4pb2/K1p2pn1/2bn1kp1/3pr1R1/6BB w - - 0 1"]

1. Rf2+! Ke3 2. Rf3+ Ke4 3. Re3+ Kd4 4. Re4+ Kd55. Rd4+ Kc5 6. Rd5+ Kc6 7. Rc5+ Kb6 8. Rc6+ Kb7 9. Rb6+ Ka7 10. Rb7+ Ka8 11. Ra7+ Kb8 12. Ra8#

The record for the longest sequence in a checkmate problem is 13, but it cannot contend for the record since Black’s king can walk out of the double checking sequence.
[Title "Dragan Stojnic & Milomir Babic, The Problemist 2004-05, Mate In 13"]
[FEN "3q1nKB/R1P1kPRB/N3p3/1p1n2p1/2r2p2/1p2b3/P2pb2N/3r4 w - - 0 1"]

1. c8=N+! Kf6 2. Rg6+ Kf5 3. Rf6+ Ke5 4. Rf5+ Ke45. Re5+ Kd4 6. Re4+ Kd3 7. Rd4+ Kc3 8. Rd3+ Kc2 9. Rc3+ Kb2 10. Rc2+ Kb1 11. Rb2+ Ka1 12. Rb1+ Kxa2 13. Nb4#


user15543: Addendum 12/30/2020: With promoted pieces allowed, I found that the below matrix apparently allows for a record of 18 forced double checks.
[FEN "BQN3N1/1RPRPk2/1B6/1p4pp/2pp3n/4p3/4K1p1/1R2N3 w - - 0 1"]

1. e8=Q+ Kxe8 2. Nd6+ Kxd7 3. c8=B+ Kc6 4. Rc7+ Kxd6 5. Rc6+ Kd5 6. Rd6+ Ke5 7. Rd5+ Ke4 8. Re5+ Kf4 9. Rf5+ Kg4 10. Rf4+ Kg3 11. Rg4+ Kh3 12. Rg3+ Kh2 13. Rxg2+ Kh1 14. Rg1+ Kxg1 15. Nf3+ Kg2 16. Ne1+ Kg1 17. Nf3+ Kg2 18. Ne1+

As such, without promoted pieces, we now have a new high of 17 forced double checks!
[FEN "BQN1kb2/1RP1r3/1B3rn1/1p4pp/2pp3n/4p3/4K1p1/1R2N3 w - - 0 1"]

1. Nd6+ Kd7 2. c8=B+ Kc6 3. Rc7+ Kxd6 4. Rc6+ Kd5 5. Rd6+ Ke5 6. Rd5+ Ke4 7. Re5+ Kf4 8. Rf5+ Kg4 9. Rf4+ Kg3 10. Rg4+ Kh3 11. Rg3+ Kh2 12. Rxg2+ Kh1 13. Rg1+ Kxg1 14. Nf3+ Kg2 15. Ne1+ Kg1 16. Nf3+ Kg2 17. Ne1+


In the time since @Evargalo posted their answer, a new record of 14 forced double checks without promoted pieces has appeared in a selfmate problem.
[Title "Miodrag Mladenovic, MatPlus.net Forum 14/11/2019, s#15"]
[FEN "BQN3N1/1RPRPk2/1B6/1b4np/2nr3r/4q3/4P1p1/4K3 w - - 0 1"]

1. e8=Q+ Kxe8 2. Nd6+ Kxd7 3. c8=B+ Kc6 4. Rc7+ Kxd6 5. Rc6+ Kd5 6. Rd6+ Ke5 7. Rd5+ Ke4 8. Re5+ Kf4 9. Rf5+ Kg4 10. Rf4+ Kg3 11. Rg4+ Kh3 12. Rg3+ Kh2 13. Rxg2+ Kh1 14. Rg1+ Kxg1 15. Qg3+ Qxg3#


user14079: I am pretty sure I could make this last longer, but here is already a sequence with 26 unforced consecutive double-checks without promoted pieces.
[FEN "8/8/8/Rp2p3/3Pk1N1/6pB/1Q2N2B/K3R3 w - - 0 1"]

1. Nc3+ Kxd4 2. Ne2+ Ke4 3. Nc3+ Kd4 4. Ne2+ Ke4 5. Nc3+ Kd4 6. Nxb5+ Kd5 7. Nc3+ Kd4 8. Nb5+ Kd5 9. Nc3+ Kd4 10. Ne2+ Ke4 11. Nxg3+ Kf4 12. Ne2+ Ke4 13. Nc3+ Kd4 14. Nb5+ Kd5 15. Nc3+ Kd4 16. Ne2+ Ke4 17. Ng3+ Kf4 18. Ne2+ Kf5 19. Nh6+ Ke4 20. Ng3+ Kf4 21. Ne2+ Ke4 22. Nc3+ Kd4 23. Nb5+ Kd5 24. Nc3+ Kd4 25. Nb5+ Kd5 26.Nc7+

12 forced double-checks, based on the scheme given by Hauke Reddmann in a comment:
[FEN "1RN5/5p2/7p/3P3p/2P3p1/QPk4N/1R1p1K2/BB6 w - - 0 1"]

1. Rc2 Kd3 2. Rc3 Kd4 3. Rd3 Ke4 4. Rd4 Ke5 5. Re4 Kf5 6. Re5 Kf6 7. Rf5 Kg6 8. Rf6 Kg7 9. Rg6 Kh7 10. Rg7 Kh8 11. Rh7 {11. Rg8} Kg8 12.Ne7


15543: <p>The <a href="https://chess.stackexchange.com/questions/8982/theoretical-limit-for-the-number-of-consecutive-checks">record</a> for the most mutual checks in a legal position is known. But what is the record for double checks? There is one rule-threefold repetition applies. Four criteria exist-promoted pieces allowed and not along with forced, Black defends, and unforced, Black helps. Below is my research.</p>
<hr />
<pre><code>[Title &quot;No Promoted Pieces, Unforced-6&quot;]
[FEN &quot;4K3/8/8/3p4/k1p1N3/1p4N1/P5BB/RRQ5 w - - 0 1&quot;]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kxd5 4. Nc3+ Kd6 5. Nf5+ Kc5 6. Na4#
</code></pre>
<hr />
<pre><code>[Title &quot;No Promoted Pieces, Forced-5&quot;]
[FEN &quot;kb1r4/P1p5/1P2P3/6NB/7B/8/8/RRQ4K w - - 0 1&quot;]

1. axb8=Q+ Kxb8 2. bxc7+ Kc8 3. cxd8=Q+ Kxd8 4. Nf7+ Ke8 5. Nd6+ Kf8
</code></pre>
<hr />
<pre><code>[Title &quot;Promoted Pieces, Unforced-9&quot;]
[FEN &quot;K5b1/5p2/4p3/3pR3/k1p1N1N1/1pQ5/P1B5/RR1R1RRR w - - 0 1&quot;]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kd7 4. dxe6+ Ke8 5. exf7+ Kf8 6. fxg8=Q+ Kxg8 7. Nh6+ Kh7 8. Nf6+ Kh8 9. Nf7#
</code></pre>
<hr />
<pre><code>[Title &quot;Promoted Pieces, Forced-8&quot;]
[FEN &quot;K4Bb1/5p2/4p3/3p4/k1p3N1/1pR5/P1B5/RQ1RRRRR w - - 0 1&quot;]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kd7 4. dxe6+ Ke8 5. exf7+ Kxf8 6. fxg8=Q+ Kxg8 7. Nh6+ Kh8 8. Nf7#
</code></pre>
<hr />
<p>Addendum: @Hauke Reddmann commented a known double checking mechanism, but no origin is given. The likely origin of it is a century old <a href="https://www.yacpdb.org/#288613" rel="nofollow noreferrer">problem</a> as @Evargalo proposed a comment.</p>
<pre><code>[Title &quot;Alain Campbell White, Pittsburgh Gazette Times 4/1916, Mate In 12&quot;]
[FEN &quot;2q5/2pp4/3pr3/4pb2/K1p2pn1/2bn1kp1/3pr1R1/6BB w - - 0 1&quot;]

1. Rf2+! Ke3 2. Rf3+ Ke4 3. Re3+ Kd4 4. Re4+ Kd55. Rd4+ Kc5 6. Rd5+ Kc6 7. Rc5+ Kb6 8. Rc6+ Kb7 9. Rb6+ Ka7 10. Rb7+ Ka8 11. Ra7+ Kb8 12. Ra8#
</code></pre>
<p>The <a href="https://pdb.dieschwalbe.de/P1373088" rel="nofollow noreferrer">record</a> for the longest sequence in a checkmate problem is 13, but it cannot contend for the record since Black’s king can walk out of the double checking sequence.</p>
<pre><code>[Title &quot;Dragan Stojnic &amp; Milomir Babic, The Problemist 2004-05, Mate In 13&quot;]
[FEN &quot;3q1nKB/R1P1kPRB/N3p3/1p1n2p1/2r2p2/1p2b3/P2pb2N/3r4 w - - 0 1&quot;]

1. c8=N+! Kf6 2. Rg6+ Kf5 3. Rf6+ Ke5 4. Rf5+ Ke45. Re5+ Kd4 6. Re4+ Kd3 7. Rd4+ Kc3 8. Rd3+ Kc2 9. Rc3+ Kb2 10. Rc2+ Kb1 11. Rb2+ Ka1 12. Rb1+ Kxa2 13. Nb4#
</code></pre>
 15543: <p>Addendum 12/30/2020: With <strong>promoted pieces allowed</strong>, I found that the below matrix apparently allows for a record of <strong>18 forced</strong> double checks.</p>
<pre><code>[FEN &quot;BQN3N1/1RPRPk2/1B6/1p4pp/2pp3n/4p3/4K1p1/1R2N3 w - - 0 1&quot;]

1. e8=Q+ Kxe8 2. Nd6+ Kxd7 3. c8=B+ Kc6 4. Rc7+ Kxd6 5. Rc6+ Kd5 6. Rd6+ Ke5 7. Rd5+ Ke4 8. Re5+ Kf4 9. Rf5+ Kg4 10. Rf4+ Kg3 11. Rg4+ Kh3 12. Rg3+ Kh2 13. Rxg2+ Kh1 14. Rg1+ Kxg1 15. Nf3+ Kg2 16. Ne1+ Kg1 17. Nf3+ Kg2 18. Ne1+
</code></pre>
<p>As such, <strong>without promoted pieces,</strong> we now have a new high of <strong>17 forced</strong> double checks!</p>
<pre><code>[FEN &quot;BQN1kb2/1RP1r3/1B3rn1/1p4pp/2pp3n/4p3/4K1p1/1R2N3 w - - 0 1&quot;]

1. Nd6+ Kd7 2. c8=B+ Kc6 3. Rc7+ Kxd6 4. Rc6+ Kd5 5. Rd6+ Ke5 6. Rd5+ Ke4 7. Re5+ Kf4 8. Rf5+ Kg4 9. Rf4+ Kg3 10. Rg4+ Kh3 11. Rg3+ Kh2 12. Rxg2+ Kh1 13. Rg1+ Kxg1 14. Nf3+ Kg2 15. Ne1+ Kg1 16. Nf3+ Kg2 17. Ne1+
</code></pre>
<hr />
<p>In the time since @Evargalo posted their answer, a new record of <strong>14 forced</strong> double checks <strong>without promoted pieces</strong> has appeared in a <a href="https://pdb.dieschwalbe.de/P1371538" rel="nofollow noreferrer">selfmate problem.</a></p>
<pre><code>[Title &quot;Miodrag Mladenovic, MatPlus.net Forum 14/11/2019, s#15&quot;]
[FEN &quot;BQN3N1/1RPRPk2/1B6/1b4np/2nr3r/4q3/4P1p1/4K3 w - - 0 1&quot;]

1. e8=Q+ Kxe8 2. Nd6+ Kxd7 3. c8=B+ Kc6 4. Rc7+ Kxd6 5. Rc6+ Kd5 6. Rd6+ Ke5 7. Rd5+ Ke4 8. Re5+ Kf4 9. Rf5+ Kg4 10. Rf4+ Kg3 11. Rg4+ Kh3 12. Rg3+ Kh2 13. Rxg2+ Kh1 14. Rg1+ Kxg1 15. Qg3+ Qxg3#
</code></pre>
 14079: <p>I am pretty sure I could make this last longer, but here is already a sequence with <strong>26 unforced</strong> consecutive double-checks without promoted pieces.</p>

<pre><code>[FEN "8/8/8/Rp2p3/3Pk1N1/6pB/1Q2N2B/K3R3 w - - 0 1"]

1. Nc3+ Kxd4 2. Ne2+ Ke4 3. Nc3+ Kd4 4. Ne2+ Ke4 5. Nc3+ Kd4 6. Nxb5+ Kd5 7. Nc3+ Kd4 8. Nb5+ Kd5 9. Nc3+ Kd4 10. Ne2+ Ke4 11. Nxg3+ Kf4 12. Ne2+ Ke4 13. Nc3+ Kd4 14. Nb5+ Kd5 15. Nc3+ Kd4 16. Ne2+ Ke4 17. Ng3+ Kf4 18. Ne2+ Kf5 19. Nh6+ Ke4 20. Ng3+ Kf4 21. Ne2+ Ke4 22. Nc3+ Kd4 23. Nb5+ Kd5 24. Nc3+ Kd4 25. Nb5+ Kd5 26.Nc7+
</code></pre>

<p><strong>12 forced</strong> double-checks, based on the scheme given by Hauke Reddmann in a comment:</p>

<pre><code>[FEN "1RN5/5p2/7p/3P3p/2P3p1/QPk4N/1R1p1K2/BB6 w - - 0 1"]

1. Rc2 Kd3 2. Rc3 Kd4 3. Rd3 Ke4 4. Rd4 Ke5 5. Re4 Kf5 6. Re5 Kf6 7. Rf5 Kg6 8. Rf6 Kg7 9. Rg6 Kh7 10. Rg7 Kh8 11. Rh7 {11. Rg8} Kg8 12.Ne7
</code></pre>
