A nonerturbative approach to such problems has been developed, based on a Liouville-space expansion of the solution of Heisenberg equation of motion for the relevant operators as a series of time-independent basis elements with time-dependent coefficients to be determined. Since the method is applicable to nonlinear dynamics of both classical and quantum systems, these two cases are treated in parallel. The necessary nonlinear dependence on initial conditions is introduced by allowing Liouvellian eigenvalues to depend on constants of motion. The formalism is illustrated by application to the anharmonic classical oscillator and the quantum Jaynes-Cummings model.