We consider a quantum-mechanical system, finite or extended, initially in its ground-state, exposed to a time-dependent potential pulse, with a slowly varying envelope and a carrier frequency \$\textbackslashomega\_0\$. By working out a rigorous solution of the time-dependent Schr\textbackslash"odinger equation in the high-\$\textbackslashomega\_0\$ 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 \$\textbackslashomega\_0ˆ\-1\\$, observables are given in terms of the linear density response function \$\textbackslashchi(\textbackslashrv,\textbackslashrv',\textbackslashomega)\$, despite the problem's 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 sphere models reveals very high surface sensitivity of NLHFPS, which produces a richer excitation spectrum than accessible within the linear-response regime. Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the conventional dipole selection rules, and the ease of theoretical interpretation by means of the linear response time-dependent density functional theory, NLHFPS has the potential to evolve into a powerful characterization method in nanoscience and nanotechnology.