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Several procedures are proposed for testing the specification of an econometric model in the presence of one or more other models which purport to explain the same phenomenon.These procedures are shown to be closely related, but not identical, to the non-nested hypothesis tests recently proposed by Pesaran and Deaton [7], and to have similar asymptotic properties..They are remarkably simple both conceptually and computationally, and, unlike earlier techniques, they may be used to test against several alternative models simultaneously.Some empirical results are presented which suggest that the ability of the tests to reject false hypotheses is likely to be rather good in practice.