  We present a method for generating solutions in some scalar-tensor theories
with a minimally coupled massless scalar field or irrotational stiff perfect
fluid as a source. The method is based on the group of symmetries of the
dilaton-matter sector in the Einstein frame. In the case of Barker's theory the
dilaton-matter sector possesses SU(2) group of symmetries. In the case of
Brans-Dicke and the theory with "conformal coupling", the dilaton- matter
sector has $SL(2,R)$ as a group of symmetries. We describe an explicit
algorithm for generating exact scalar-tensor solutions from solutions of
Einstein-minimally-coupled-scalar-field equations by employing the nonlinear
action of the symmetry group of the dilaton-matter sector. In the general case,
when the Einstein frame dilaton-matter sector may not possess nontrivial
symmetries we also present a solution generating technique which allows us to
construct exact scalar-tensor solutions starting with the solutions of
Einstein-minimally-coupled-scalar-field equations. As an illustration of the
general techniques, examples of explicit exact solutions are constructed. In
particular, we construct inhomogeneous cosmological scalar-tensor solutions
whose curvature invariants are everywhere regular in space-time. A
generalization of the method for scalar-tensor-Maxwell gravity is outlined.
