  We study a general Scalar-Tensor Theory with an arbitrary coupling funtion
$\omega (\phi )$ but also an arbitrary dependence of the ``gravitational
constant'' $G(\phi )$ in the cases in which either one of them, or both, do not
admit an analytical inverse, as in the hyperextended inflationary scenario. We
present the full set of field equations and study their cosmological behavior.
We show that different scalar-tensor theories can be grouped in classes with
the same solution for the scalar field.
