We have measured the response of the vortex system in the low Tc superconductor 2H-NbSe2 to finite frequency drives. In a well-defined range of fields, temperatures, and driving amplitudes the system exhibits novel nonlinear phenomena. Most strikingly, the vortices can move easily in response to currents that are well below the dc critical current if the direction of the current is reversed periodically while the amplitude I is kept fixed, but they do not respond to a current that periodically switches between zero and I, while the direction is kept fixed. Pronounced memory effects associated with these phenomena indicate the presence of dynamically generated structural changes in the vortex array.