A class of distribution-free tests for testing independence against positive quadrant dependence has been proposed by Kochar and Gupta(1987). In this paper,we consider a test of independence against orthant dependence. The proposed test is a generalization of Kochar and Gupta's tests to one multivariate dependence case. Also,we investigate two multivariate extensions of Kendall's tau as two competitors of this generalized class. The frst option, developed byJoe (1990), is a direct generalization of Kendall's tau in the bivariate case and is based on Kochar and Gupta's approach. The second one, introduced by Kendall and Babington Smith (1940), is a coefficient of agreement defind as the average value of Kendall's tau taken overall possible pairs of variables. Finally,we compare the empirical power of multivariate extensions of Kendall's tau with that of the generalization of Kochar and Gupta's tests.

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