It is a difficult problem to test the equality of distribution of two independent p-dimensional (p>1) samples (of sizes m and n, say) in a nonparametric framework. It is not only because we need deal with issues such as tractability of the null distribution of test-statistics but also the fact that the latter are rarely distribution-free. Several notable nonparametric tests for comparing multivariate distributions  are the multivariate runs test of Friedman and Rafsky (1979), the nearest-neighbour test of Henze (1988) and the inter-point distance-based test of Baringhaus and Franz (BF) (2004). Biswas and Ghosh (BG) (2014) recently have shown that in a high dimension, low sample-size (HDLSS) scenario, i.e. where p goes to infinity but m, n are small or fixed, all the tests mentioned do not perform well. However, the BG-test is shown to be consistent in the case of HDLSS. In this work, we study the asymptotic behaviours of BF and BG tests when m, n and p go to infinity and min(m, n) = o(p). Our results reveal when these tests are expected to work well and when they are not. Results are illustrated by simulated data.