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This paper describes the package PtProcess which uses the R statistical language. The package provides a unified approach to fitting and simulating a wide variety of temporal point process or temporal marked point process models. The models are specified by an intensity function which is conditional on the history of the process. The user needs to provide routines for calculating the conditional intensity function. Then the package enables one to carry out maximum likelihood fitting, goodness of fit testing, simulation and comparison of models. The package includes the routines for the conditional intensity functions for a variety of standard point process models. The package is intended to simplify the fitting of point process models indexed by time in much the same way as generalized linear model programs have simplified the fitting of various linear models. The primary examples used in this paper are earthquake sequences but the package is intended to have a much wider applicability.