The authors show that, contrary to the beliefs of some previous analysts of international economic growth, the hypotheses of convergence and of mean-reversion are not equivalent. Under some assumptions, the rate of convergence is independent of the degree of mean-reversion; under other assumptions, mean-reversion is a necessary, but not a sufficient, condition for convergence. The authors show the relationship between the convergence test and the mean-reversion test and provide an empirical example in which the null hypothesis of no mean-reversion is rejected but the null hypothesis of no convergence is not rejected.