A pulsed dye laser system with a narrow-band signal injected into the cavity is considered. The injection starts prior to the excitation pulse. It is shown that during a transient period, injection locking can be achieved for a much wider range of parameters than under conventional CW conditions. The analysis is based on a set of coupled rate equations for the population densities and photon fluxes at all wavelengths. These are solved numerically with appropriate initial and boundary conditions. Analytical approximations, which are helpful for understanding the behavior of such systems, are presented. Both straight, two-mirror cavities, and ring laser cavities are discussed. The temporal evolution of the spectral components at all wavelengths is described. The range of tunability in this mode of operation and its dependence on various parameters, such as pulse length, cavity dimensions, and injection intensity are discussed.