A perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state. The expansion is expressed directly in terms of the kinetic parameter (creation rate), rather than in powers of the interaction. An algorithm for generating series expansions for local properties is described. Order parameter series (16 terms) and precise estimates of critical properties are presented for the one-dimensional contact process and several related models.