The nonlinear response of a Vlasov plasma has been calculated numerically for several externally applied electric field configurations. In the presence of a standing wave of frequency&ohgr;0≳ &ohgr;pe, the energy of the particle distribution and the envelope of the particle electric field were found to oscillate slowly with approximately the period of the trapped particles. Analogous spatial oscillations have been reported by Malmberg and Wharton. Bernstein, Greene, and Kruskal equilibria were calculated for a constant, sinusoidal inhomogeneity in the background ion charge density and found to be numerically stable against small perturbations. Landau‐damping rates for the perturbations are compared with the calculations of Jackson and Raether. In the presence of a slowly varying(&ohgr;0≪ &ohgr;pe)inhomogeneous background (simulating an ion acoustic wave) the electrons were found to obey a locally isothermal equation of state to within a few percent for the times that could be calculated. The response of an initially uniform plasma to a suddenly applied external field was also calculated.