  Recent astrophysical observations indicate that the proton-electron mass
ratio and the fine structure constant have gone through nontrivial time
evolution. We discuss their time variation in the context of a dilaton runaway
scenario with gauge coupling unification at the string scale $M_{\rm s}$. We
show that the choice of adjustable parameters allows them to fit the same order
magnitude of both variations and their (opposite) signs in such a scenario.
