Asymptotic small-parameter expansion is applied to the solutions for singularly perturbed systems in order to examine the kinetics of laser excitation for nonequilibrium carriers and excitons in silicon and germanium crystals, which incorporates nonequilibrium carrier recombination, linear recombination, and exciton formation and ionization. Asymptotic evaluations can be used that apply throughout the range in pulse length in order to provide indirect and rough estimates of the probabilities for various recombination and ionization processes.