Semianalytic perturbative approaches for investigating the spectroscopy, and the underlying dynamics, associated with fast time-resolved, two-photon, two-color, pump-probe, low intensity laser-molecule interactions are developed and discussed. In particular the perturbation theory is developed with emphasis on molecular models associated with pump-probe experiments on the S-0-->S-1-->S-2 two-photon transitions in azulene and trimethylazulene. The experiments are discussed and the theory is used to determine the lifetimes of the intermediate S-1 states by analyzing the experimental two-photon fluorescence signals from the S-2 states as a function of the time-delay between the pump and probe lasers. The advantages of using this approach relative to the traditional methods for determining the lifetime of the S-1 states are discussed. The dependence of the two-photon fluorescence signals on the angle between the polarization vectors of the pump and probe lasers, for fixed time delay between the lasers, is also considered briefly.