  All classes of spatially homogeneous space-time models in the generalized
scalar-tensor theory of gravity are found that allow the integration of the
equations of motion of test particles and the eikonal equation by the method of
%complete separation of variables by type (3.1). Three classes of exact
solutions are obtained that relate to wave-like spacetime models. The resulting
spacetime models are of type IV, VI, and VII according to the Bianchi
classification and type N according to Petrov's classification.
