It's not
quite the longest-running edition, but it's very close.
BECMI began with Frank Mentzer's
Basic Set (the "B" in "BECMI"), which, presuming I have my dates correct, came out on May 1st, 1983. After this, the absolute latest I can find a BECMI-compatible product coming out from TSR is Troy Denning's
The Classic Dungeons & Dragons Game: Epic Adventures with Wizards, Dragons, and Magic!, which came out on either May 2nd or May 4th, 1994 (I've seen conflicting listings). So BECMI lasted almost exactly eleven years.
(If you don't count that introductory boxed set as the ending point, then the last BECMI product would be the
Poor Wizard's Almanac II, published on December 1st, 1993.)
By contrast, the AD&D 2E
Player's Handbook came out in February of 1989, with the
Dungeon Master's Guide following in May of the same year and the
MC1 Monstrous Compendium Volume One following in June (I can't find exact release dates). Since the last AD&D 2E product was
Die Vecna Die! (June, 2000), that means that if you start counting from when the PHB was released, AD&D 2E just barely edges out BECMI by a few months.
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