What amp should I buy to power Martin Logan Esl's?

Best ML sound I have heard was off a Krell integrated amp about 4 years ago. I also heard a pair of Focal Profile 918s on the same system and both sounded very good. It was a very lively and decent sized Twitter listening room. Holography was off the scale with both.

Whoops, obviously that was a "Tweeter" store, not twitter......

Best ML sound I have heard was off a Krell integrated amp about 4 years ago.

funny as that was my experience as well. the best M-L sound I heard was Krell FPB600 monos driving the M-L Statement E2 speaker. Krell CDP & Krell preamp. MIT cables. That was in the Sound Advice showroom when Gail Martin Sanders himself was touring the country doing these demos.
I still remember the sound today-absolutely fantastic! I wanted to run out & buy that exact system right there & then! Alas, when I was presented the bill I saw that it was in unobtainium land....;-0

Source on that system was a krell CD player as well. ICs and speaker wires were all Audioquest I am pretty sure.

I wouldn't discount tube amps in regard to driving ESL hybrids such as Martin Logan or a pure ESL such as Quad. The combination can be quite magical as a matter of fact. In years gone by I used a nominally 40 wpc (probably more like 25 wpc in actuality) Class A single ended parallel pentode 5881/6L6 amp to drive ML Aerius speakers and it sounded simply wonderful if a little lacking in dynamics at times. Switched to an EL34 push/pull amp from the same company putting out 100wpc and the Aerius speakers gained in dynamics if a bit less detail. I've driven Quad 989s with both 70 wpc and 140 wpc conrad-johnson tube amps (Premier 11A and Premier 140) and they both made beautiful music with the Quads.

Granted, as a previous poster stated, the Quads are a more benign load than the ML. However, just because a certain pairing may look great or not so great on paper isn't always an indication of what it's actually going to sound like. So much of it is system dependent and a matter of personal taste that blanket statements may be misleading.

Just my 2¢ naturally.