We examine a new general class of hazard rate models for durationdata, containing a parametric and a nonparametric component. Bothcan be a mix of a time effect and possibly time-dependent covariate effects. A number of well-known models are special cases. In a counting process framework, a general profile likelihood estimator is developed and the parametric component of the model is shown to be asymptotically normal and efficient. Finite sample properties are investigated in simulations. The estimator is applied to investigate the long-run relationship between birth weight and later-life mortality.