  We discuss the effects of a possible time variation of the Newton constant
$G_{\rm N}$ on light elements production in Big Bang Nucleosyntesis (BBN). We
provide analytical estimates for the dependence of primordial abundances on the
value of the Newton constant during BBN. The accuracy of these estimates is
then tested by numerical methods. % Moreover, we determine numerically the
response of each element to an arbitrary time-dependent modification of the
early universe expansion rate. Finally, we determine the bounds on possible
variations of $G_{\rm N}$ which can be obtained from the comparison of
theoretical predictions and observational data.
