  We estimate the possible variations of the gravitational constant G in the
framework of a generalized (Bergmann-Wagoner-Nordtvedt) scalar-tensor theory of
gravity on the basis of the field equations, without using their special
solutions. Specific estimates are essentially related to the values of other
cosmological parameters (the Hubble and acceleration parameters, the dark
matter density etc.), but the values of G-dot/G compatible with modern
observations do not exceed 10^{-12}.
