Observables in nonlinear spectroscopic measurements may be calculated from response functions, which have the form of averages of nested commutators involving the operator governing the radiation-matter interaction. We present a semiclassical formulation of the optical nonlinear response function, employing the Herman-Kluk frozen Gaussian approximation to the quantum propagator in the coherent states representation. This semiclassical approximation permits the response function to be computed from classical trajectories and stability matrices, and provides insight into the relationship between nonlinear response in classical and quantum mechanics. Linear response calculations for an anharmonic oscillator illustrate that the semiclassical approach reproduces the significant differences between quantum and classical results. (C) 2003 American Institute of Physics.