  A variation of the gravitational constant over cosmological ages modifies the
main sequence lifetimes and white dwarf cooling ages. Using an state-of-the-art
stellar evolutionary code we compute the effects of a secularly varying G on
the main sequence ages and, employing white dwarf cooling ages computed taking
into account the effects of a running G, we place constraints on the rate of
variation of Newton's constant. This is done using the white dwarf luminosity
function and the distance of the well studied open Galactic cluster NGC 6791.
We derive an upper bound G'/G ~ -1.8 10^{-12} 1/yr. This upper limit for the
secular variation of the gravitational constant compares favorably with those
obtained using other stellar evolutionary properties, and can be easily
improved if deep images of the cluster allow to obtain an improved white dwarf
luminosity function.
