The Zelwail-Bersohn model [Ber. Bunsenges. Phys. Chem. 92, 373 (1988)] of pump-probe experiments is generalized to nonstationary wave packets and more realistic forms of probe pulses. The analysis illustrates the important role of probe linear chirp rare, as pointed out by Sterling, Zadoyan, and Apkarian [J. Chem. Phys. 104, 6497 (1996)], in detecting the motion of wave packets and the physical reason for the existence of optimal probe pulses to yield the best probe signal. Since the pump-probe process can be viewed as delayed two-photon resonant absorption, the probe signal can be readily optimized within the framework of quantum control theory, as-discussed by Yan [J. Chem. Phys. 100, 1094 (1994)]. Numerical calculations based on quantum control theory are used to confirm our theoretical predictions. We point out that the same analysis can be extended to other impulsive nonlinear optical processes, such as multiphoton pump-probe absorption and stimulated Raman scattering.