Steely Dan

James Taylor--Sweet Baby James is even better than his first.  

Anubis


Chicago I and II.

Yeah ... really hard to disagree with this one ... very good choice! I still love listening to the double album all the way through!

space_cowboy

ricstudioc


The Tubes.

white punks on dope/mondo bondage 
dont touch me there/slipped my disco


wow what a great combo.
bring back the tubes

It was the only album of theirs that is a total kick ... and you can put it on full blast and LOUD from the first cut ... that introduction is fantastic too! But it has been said that it worked because of Dominic Frontiere.

but it doesn't fit the criteria.... 

sure it does, to a tee!!
so, another nomination would be:

Brand X, Unorthodox Behaviour, Morrocan Roll

batsbrew

but it doesn't fit the criteria.... 

sure it does, to a tee!!
so, another nomination would be:

Brand X, Unorthodox Behaviour, Morrocan Roll

If you want to believe that those were better than Electric Ladyland it's fine by me.
 

well, actually, no, i don't!

but i think JH's first two albums, was an example of a band that produced one of the best pairs of 'first two albums', that stand the test of time.


a 3rd album, and it's impact, was not part of the OP's original request.

in my mind, it's a real simple concept.
and not one to hung about.


as for brand x, two great 1st albums, they rock.

other honorable mentions:

VHI and II
The Doors & Strange days
My aim is true & This year's model
Chicago Transit Authority & Chicago
Santana & Abraxas
The cars & Candy-O
Texas Flood & Couldn't Stand the Weather
Aerosmith & Get your Wings
Rage against the machine & evil empire
Talking heads:77 & more songs about buildings and food

"what bands do you think produced the best first two albums?  So many seem to stumble after a great original effort"

The way I read it Bat...is what bands stumble after a couple of good releases.
You read it differently and that much is certain. Carry on.

batsbrew


other honorable mentions:

My aim is true & This year's model
 

Well remembered!  And if we're going back to that era, I'd also nominate Graham Parker and the Rumor: Howlin' Wind followed by Heat Treatment.