We consider the problem of estimating the life-distribution F from censored lifetimes. The observation scheme is renewal testing over a long time horizon although the results can apply to survival testing with repetitions. We exhibit a product-limit estimator of F which is shown to be consistent and to converge weakly to a GAUSsian process. To do this we first extend these properties of the NELSON-AALEN martingale estimator to the family of PoissoN-type counting processes. Our proof of weak convergence is based on the general functional central limit theorems for semimartingales as developed by .JACOB, SHIRYAYEV and others