  In the context of a family os scalar-tensor theories with a dynamical
$\Lambda$, that is a binomial on the scalar field, the cosmological equations
are considered. A general barotropic state equation $p=(\gamma-1)\rho$, for a
perfect fluid is used for the matter content of the Universe. Some Friedmann-
Robertson-Walker exact solutions are found, they have scale factor wich shows
exponential or power law dependence on time. For some models the singularity
can be avoided. Cosmological parameters as $\Omega_m$, $\Omega_{\Lambda}$,
$q_0$ and $t_0$ are obtained and compared with observational data.
