A two-stage procedure for survival studies with surrogate endpoints is proposed. The objective of the procedure is to reduce the duration of a survival study relative to classical procedure. A surrogate endpoint is an event which is related to survival time and may occur earlier during follow up. In the first stage, all patients are followed to the primary endpoint in order to evaluate the strength of the relationship between the surrogate endpoint and survival. In the second stage, follow up is terminated on patients who reach the surrogate endpoint. Indirect inferences on the survival endpoint is now possible by virtue of the first stage analysis. We present methods for data collected in the two-stage procedure, for estimating the survivorship function, S(t), and for comparing two treatment groups using a non-parametric permutation test. The methods are applied to the results of a study of resected lung cancer.