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A model describes the joint distribution of paired survival times based on certain reasonable assumptions appropriate for biological data generated in a clinical trial setting or for certain failure data. An exact parametric test for equality of mean survival times for data following this distribution is developed. The power of the exact test is investigated by a computer simulation study for various sample sizes and values of the model parameters and compared to that of alternative tests. Heretofore, researchers desiring to analyze paired survival data have resorted to paired t tests or nonparametric procedures such as the sign test or signed ranks test. The t-test is invalid for non-normally distributed data although the robustness of the test might minimize the difficulty. The nonparametric tests, by their nature, fail to use the data completely. This paper presents an exact parametric test based on a distribution whose justification requires rather modest and reasonable assumptions. Critical values for the test can be obtained from a table of the chi-square distribution. This exact test appears to be a viable alternative to non-parametric approaches to the analysis of paired survival data. It is extremely easy to calculate on a hand calculator. In fact, since no data storage is required (unlike the signed ranks test), the calculations can be readily programmed on a programmable calculator. The modeling of bivariate and multivariate survival data we believe has not been adequately addressed in the statistical and engineering literature. We hope that this paper will spark additional work.