Testing theories that predict time variation of fundamental constants

We consider astronomical and local bounds on time variation of fundamental constants to test some generic Kaluza-Klein-like models and some particular cases of Beckenstein theory. Bounds on the free parameters of the different theories are obtained. Furthermore, we find that none of the proposed models, is able to explain recent results [Webb99,Webb00] claiming an observed variation of the fine structure constant from quasar absorption systems at redshifts $0.5<z<3$.