Spectroscopic observables are governed by the dynamics on the ground and excited potential energy surfaces. An inversion scheme is presented to iteratively construct the potential surface which reproduces experimental data. Special attention is drawn to the nonlinear character of the inversion problem and, in particular, to the role of ultrafast pump-probe spectroscopy for dealing with it. The regions of inversion, Le., the nuclear configurations for which the potential is to be determined, are

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... identified by calculating the observablepotential sensitivity function. A method is introduced for calculating these sensitivity functions in a numerically converged time-dependent quantum mechanical fashion. These functions are the basic building blocks of the inverted potential. Two demonstrations of the procedure are presented, both use simulated pump-probe spectroscopic data. The first, applied to the ICN molecule, reconstructs the medium-and long-range parts of the dissociative excited surface. The second attempts to reconstruct the bound excited potential surface of NCO.