Advancing monsters

[Ywvbevlin]

Monsters can be advanced by adding racial HD or class levels. My question is if both methods can be used on the same monster.

[Necroticplague]

Yes. That's like advancing a creature by adding a template then adding class levels.

[Thurbane]

I'm pretty sure there's no rules that say both can't be applied to the same creature - I've certainly done so in my own games.

[One Step Two]

Usually the monster entries will specify how they advance, but they aren't hard and fast rules.
Here's the Bodak as an example, which advances using hit dice. Whereas the Rakshasa advances by character class.
That's not to say it can't have both. It usually comes down to perference and flavour, a prime example is the Hound Archon which has both notes on its' HD advancement, as well as the 11th level paladin variant.

For the sake of advancement though, they need to be an intelligent creature to have class levels, as outlined in the Improving Monsters section of the SRD.

[Khedrac]

Obligatory mention of Urpriest's Monstrous Monster Handbook.

Seriously it is well worth a read - Urpriest has done an excellent job of explaining monster advancement and collating the rules for it.