An approximate theory of femtosecond spectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck-Condon approximation to the case of nonadiabatic dynamics. Explicit expressions for various time- and frequency-resolved spectra are derived which allow for a simple interpretation of femtosecond spectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing (i) the nonadiabatic cis-trans isomerization of an electronic two-state system, and (ii) the S-2--> S-1 internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as time-resolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe-pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump-probe simulations to the costs of a standard time-dependent wave-packet propagation, the approximate theory leads to substantial computational savings. (C) 2000 American Institute of Physics. [S0021-9606(00)01310-6].