Bekenstein model and the time variation of the strong coupling constant

We propose to generalize Bekenstein model for the time variation of the fine structure "constant" $\alpha_{em}$ to QCD strong coupling constant $\alpha_S$. We find that, except for a ``fine tuned'' choice of the free parameters, the extension can not be performed trivially without being in conflict with experimental constraints and this rules out $\alpha_S$ variability. This is due largely to the huge numerical value of the QCD vacuum gluon condensate when compared to the matter density of the universe.