  We present a detailed calculation of the light element production in the
framework of Scalar-Tensor (ST) theories of gravitation. The coupling function
\omega has been described by an appropriate form which reproduces all the
possible asymptotic behaviors at early times of viable ST cosmological models
with a monotonic \omega(\Phi). This form gives an exact representation for most
of the particular theories proposed in the literature, but also a first-order
approximation to many other theories. In most of ST theories, the
nucleosynthesis bounds lead to cosmological models which do not significantly
differ from the standard FRW ones. We have found however a particular class of
ST theories where the expansion rate of the universe during nucleosynthesis can
be very different from that found in GR, while the present value of \omega is
high enough to ensure compatibility with solar-system experiments. In the
framework of this class of theories, right primordial abundances can be
obtained for a baryon density range much wider (2.8 \lesssim \eta_{10} \lesssim
58.7) than in GR. Consequently, the usual constraint on the baryon contribution
to the density parameter of the universe can be drastically relaxed (0.01
\lesssim \Omega_{b0} \lesssim 1.38) by considering these gravity theories. This
is the first time that a ST theory is found to be compatible both with
primordial nucleosynthesis and solar-system experiments while implying
cosmological models significantly different from the FRW ones.
