We consider a quantum-mechanical system, initially in its ground-state, exposed to a time-dependent potential pulse, with a slowly varying envelope and a high carrier frequency. By working out a rigorous solution of the time-dependent Schrodinger equation in the high-frequency limit, we show that the linear response is completely suppressed after the switch-off of the pulse. We show, at the same time, that to the lowest order in the inverse frequency, observables are given in terms of the linear density response function, despite the problem's inherent nonlinearity. We propose a new spectroscopic technique based on these findings, which we name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). An analysis of the jellium slab and jellium sphere models reveals very high surface sensitivity of NLHFPS, which produces a richer excitation spectrum than accessible within the linear regime. Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the conventional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS emerges as a powerful characterization method in nanoscience and nanotechnology.