Let (Xi,Yi), i=1,...,n be a random sample from an unknown continuous bivariate distribution H(x,y) with marginals F(x) and G(y). The paper wishes to test the null hypothesis that F=G. Asymptotic normality of the class of test statistics considered by Govandarajulu is established which enables us to construct asymptotically distribution-free tests for equality of marginals. These results are extended to the c-variate case and the case when the sample size n is random.
