  We consider a cosmological model with a variable gravitational constant, G,
based on a scalar-tensor theory. Using the recent observational data for the
Hubble diagram of type Ia supernovae (SNeIa) we find a phenomenological
expression describing the variation of G. The corresponding variation of the
fine structure constant \alpha within multidimensional theories is also
computed and is shown not to support known constraints on \Delta \alpha /
\alpha.
