In the context of a family of scalar-tensor theories with a dynamical Lambd
a that is a binomial on the scalar field, the cosmological equations are co
nsidered. A general baryotropic state equation p = (gamma - 1)rho, for a pe
rfect fluid is used for the matter content of the Universe. Some Friedmann-
Robertson-Walker exact solutions are found; they have a scale factor which
shows exponential or power law dependence on time. For some models the sing
ularity can be avoided. Cosmological parameters such as Omega(m), Omega(Lam
bda), q(0), and t(0) are obtained and compared with observational data [S05
56-2821(99)00220-9].