At least I’m pretty sure that’s him.
Sorry, the pic is a screen shot from YouTube, it’s pretty fuzzy.
Here.
Melodica, I think. You can’t see the keys because they’re on the side away from the camera.
Seconded. His left hand is holding it by the strap underneath (as intended), and his right is playing the keys. He is, of course, basically a keyboardist, so it makes sense. Here is a picture from a better angle of someone playing one. (They come in various colors and lengths.)
I’m sure you’re right. Thanks!
Even without looking at the pics (I always have trouble viewing pics on photobucket), can we agree that the default answer is always “Didgeridoo”? 
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Moving thread from General Questions to Cafe Society.
Didgeridoo? Sure, but that is an odd way to spell hurdy gurdy.
Take a look at him playing it. BTW, I’m almost positive that is an acoustic theremin.
As one of the resident Danophiles, I can say definitively that it’s a melodica.
In concert, Fagen plays it sparingly on a few numbers but he uses it mainly as a prop as he needs something to hold in his hands while singing.
Fagen is one of those performers who really doesn’t know how to work a microphone like, say, Steven Tyler or Roger Daltry. So when Fagen emerges from his keyboard for certain numbers, he keeps the melodica cradled awkwardly on his left shoulder. In years past, Fagen used one of those funky keytars which he never played a note on but again used it as a prop more than anything else.
Fagen plays the thing decently enough. What’s disappointing to me is that my all-time favorite Steely Dan song (and album) is Aja. In concert during the long instrumental section, Fagen plays the vibes part on his melodica. It simply doesn’t stack up to the original recording.