We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state, which is absorbing. We present several methods for deriving series for the evolution starting from a single seed particle, including expansions for the ultimate survival probability in the super- and subcritical regions, expansions for the average number of particles in the subcritical region, and short-time expansions. Algorithms for computer generation of the various expansions are presented. Rather long series (24 terms or more) and precise estimates of critical parameters are presented.