Can Demons and Devils have class levels?

[sukael]

And the power of the beasty should never be more than the next step up in the evolutionary chain. Why would a CR5 demon with 10 levels of barbarian want to lose power by progress up to a less powerful CR7 demon with no class levels? I could see one taking 3 levels of barbarian but any more progression than that should be to a new form. (those are just random numbers as I am no place close to a MM)

Fiendish Codex II, page 10, has the big chart of devil stages; not sure where there's an equivalent one for demons. To note, devils can jump up more than one stage at a time, so you could go, say, from a chain devil fighter 2 (CR 8) straight to an orthon (CR 8) or a bone devil (CR 9), skipping the harvester devil (or pain devil) and amnizu stages in-between.