This article describes a generalized moments specification test of the semiparametric proportional hazards model of Cox. In contrast to other specification tests for this model, the generalized moments test is applicable in the presence of continuous explanatory variables and does not require assigning the data to predetermined cells. The results of a Monte Carlo investigation suggest that the generalized moments test has good finite-sample properties and that it is more powerful than other available tests for models with continuous explanatory variables when the alternative is an accelerated failure time model. The test is based on generalized residuals for the proportional hazards model. When the model is correct, the generalized residuals have asymptotically the (possibly censored) unit exponential distribution. The generalized moments are means of functions of the generalized residuals. The generalized moments have known values when the generalized residuals have the unit exponential distribution, and an asymptoticχ2statistic tests for whether the differences between sample analogs of the generalized moments and the known values are larger than can be explained by random sampling errors.