  A new class of integrable two-dimensional dilaton gravity theories, in which
scalar matter fields satisfy the Toda equations, is proposed. The simplest case
of the Toda system is considered in some detail, and on this example we outline
how the general solution can be obtained. Then we demonstrate how the wave-like
solutions of the general Toda systems can be simply derived. In the dilaton
gravity theory this solutions describe nonlinear waves coupled to gravity. A
special attention is paid to making the analytic structure of the solutions of
the Toda equations as simple and transparent as possible, with the aim to apply
the idea of the separation of variables to non-integrable theories.
