A class of probability models for earthquake occurrences, called short-term exciting, long-term correcting (SELC) models, is presented. This class encompasses features of two different classes of models presently used in hazard analysis to characterize earthquake catalogs: (1) self-exciting models and (2) self-correcting models. It offers the potential for a unified approach to the analysis and description of different types of earthquake catalogs. Maximum likelihood estimation methods for the seismicity model parameters and standard errors are presented. Sample SELC models are shown to provide satisfactory fit to a seven-year catalog of microearthquakes occurring in Parkfield, California, and a longer seismicity sequence from the San Andreas fault zone in central California. Inferences on seismicity patterns and mechanisms are discussed. Both significant clustering and strain release are detected. The suggested procedure should lead to improved seismic hazard analysis and mapping.