In this paper the consistency of the two-sample tests of Sukhatme [6], Ansari and Bradley [1], Siegel and Tukey [5], and Mood [3] is investigated. Each of these tests is a distribution-free analogue of theF-test for testing the equality of the variances of two normal distributions. If the two samples are taken from continuous distributions with the same median (say 0) and distribution functionsF(x) andF(x/a) respectively, the hypothesis tested states thata= 1 and the two-sided tests are consistent fora≠ 1. If, however, the samples are from continuous distributions with the same median 0 and arbitrary distribution functionsFandG, little is known about their asymptotic properties. In this paper the conditions for consistency for this case are given; further it is investigated if the corresponding estimates of differences in dispersion satisfy the usual properties of measures of dispersion, namely 1) thatXand −Xhave the same dispersion and 2) that, ifXhas a larger (or equal or smaller) dispersion thanY, − Xhas a larger (or equal or smaller) dispersion thanY.