Talk to an accountant for this - if there is double taxation prevention treaty in between these 2 countries, you will taxed only once in one of them.
considering how there was recently an amnesty in spain for immigrants who did not declare their income abroad (retirement included), it seems spain expects you to register for tax here.
your situation may be specific - depending on laws, regulations affecting your particular situation in usa - whatever they may be - you may have to approach this differently.