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This paper describes how the classical set-up for censored failure time data can be reformulated in a counting process framework. Asymptotic distributional results for the maximum likelihood estimator for a general parametric counting process model are derived. From these we get the properties of the maximum likelihood estimator for censored failure time data under quite general censoring patterns. The general results are illustrated by a study of the occurrence/exposure rates and of a multiplicative model. Extension to the case where explanatory variables are included, is also considered.