In a recent interview by CC Rock, Dream Theater vocalist James LaBrie explained song writing process of Dream Theater. He said (transcribed by UG):

“Here’s what I’ve always said – piano and guitar are the primary instruments for writing. So John Petrucci and Jordan – as it currently is – are the primary writers.

It doesn’t say that myself and Mike [Mangini] and John [Myung] don’t get involved. We do, absolutely. But I think that’s always been the case right from the very beginning of Dream Theater, even when Kevin Moore was there [between 1985 and 1994].

A lot of the seeds always came from those two. And yes, other members have always got involved and said, ‘Let’s try this and try that.’

However, you go about interacting with one another and composing and putting something together. And that still kind of exists today. There’s that interaction when it comes to composing. Like I’ve said – it’s always been that the riffs and melodies that seem to stem from those instruments.

And not to say that somebody else isn’t coming in and going, ‘Here’s an idea that I have,’ or feeding off of somebody’s melody, or feeding off even a lyrical idea – these things also play into it.”

You can watch the entire interview from here.