Can you multiclass and use 2 different core class archetypes?

Question

Can you multiclass and use 2 different core class archetypes, e.g. Fighter and Ranger archetypes, assuming no replaced skills overlap? Or are archetypes only for your first class - the one you choose at lvl1?
Say I start as a Ranger and select one of his/her archetypes, then at lvl 6 or so I decide I wanna be a rogue, can I select a rogue archetype?

I've been reading that other question where someone else asks about the fighter being able to multiclass into a fighter archetype, which isn't quite the same thing. He/she is basically asking if he can have multiple archetypes of the class he started with, while I wanna know if you can have archetypes of totally different classes.

Do I need to declare at creation (lvl1) my will to take an archetype in a class I plan to take later on?

Answer 1

From the Pathfinder SRD:

A character can take more than one archetype and garner additional alternate class features, but none of the alternate class features can replace or alter the same class feature from the base class as another alternate class feature. For example, a fighter could not be both an armor master and a brawler, since both archetypes replace the weapon training 1 class feature with something different.

There is nothing else specifically related to the rest of your question on that page, so the rest of my answer is based on my interpretation, which may or may not be shared by your GM.

My understanding is that you select any archetypes that you wish to take for a class the first time you take a level in that class. For example, if you had a character with Ranger 6/Rogue 1, you would select your Ranger archetypes at level 1, while you would select your Rogue archetypes at level 7 (your first level of Rogue). Since class features are not shared between base classes (even if the ability has the same name in both), there are no concerns about overlapping changes from archetypes.

Answer 2

As the Pathfinder SRD tells us, each and every archetype basically changes the class features of a class. Different archetypes can be combined provided they don't remove the same class feature from the original base class.

When you get a different class by multiclassing, you can apply that class' archetypes to the new class as soon as you take it. Since the archetypes modify the features of a class, each class is handled separately for the qualifications.

Just as you don't need to plan in advance your multiclassing, you don't need to choose your archetypes before you get a level in that class. But as soon as you get that level, you need to say which archetypes you want to take for that class.