Experiments in which the measured responses are times until events occur are common in a variety of fields. When only one response is measured on each subject, the proportional hazards model of Cox (1972) is often used to assess the effects of one or more explanatory variables on the event times. Two new resampling plans are introduced for bootstrapping estimators from this model when explanatory variables are fixed by design. One method resamples from the Uniform (0,1) distribution of the probability integral transformation corresponding to the conditional failure time distribution, and it is easily adapted to a wide variety of censoring schemes. The other method is an analog to the residual-resampling method for regression introduced by Efron (1979), and it admits random censoring from a class of distributions which includes the Koziol-Green model;Multivariate extensions of resampling methods are developed for situations where multiple event times are monitored on individual subjects. Marginal models are fit using an independence working model approach. Resampling procedures are then applied to the joint distribution of the multiple responses or residuals to make bias corrections to the parameter estimates, estimate covariance matrices, and construct confidence intervals. Simulation studies indicate that each of the proposed methods provides substantial improvements in mean squared errors over existing techniques for estimation of model parameters. The proposed methods also provide better estimates of standard errors and more reliable confidence intervals for model parameters than existing methods which rely largely on asymptotic approximations. These methods are demonstrated through applications to data sets available in the literature.