  We formulate a renormalization group approach to a general nonlinear
oscillator problem. The approach is based on the exact group law obeyed by
solutions of the corresponding ordinary differential equation. We consider both
the autonomous models with time-independent parameters, as well as
nonautonomous models with slowly varying parameters. We show that the
renormalization group equations for the nonautonomous case can be used to
determine the geometric phase acquired by the oscillator during the change of
its parameters. We illustrate the obtained results by applying them to the Van
der Pol, and Van der Pol-Duffing models.
