We consider nonparametric estimation of bivariate distribution functions, and more generally transition probabilities from censored duration times of successive events. The model differs from standard bivariate censoring models in that censoring and sojourn times form dependent variables and as a result of it parameters arising in many survival function estimates fail to be asymptotically identifiable. Averaged Beran's conditional Kaplan-Meier estimate is shown here to yield a consistent estimate of transition probabilities. A standardized version of the estimate behaves asymptotically as a Gaussian process which can be represented in terms of stochastic integrals with respect to one and two-parameter Brownian Motions. The result is used to construct tests for independence of successive duration times and illustrated on data from an AIDS study.