The paper derives and compares the local power of three different methods of testing non-nested regression models that are available in the literature. It shows that the asymptotic power of the orthodox F test against local alternatives is strictly less than that of Cox's non-nested test or the J test recently proposed by Davidson and MacKinnon [5], unless the number of non-overlapping variables of the alternative hypothesis over the null hypothesis is unity, in which case all three tests are shown to be asymptotically equivalent. The final section of the paper gives results of Monte Carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the Cox test and the orthodox test.