This paper is concerned with a problem of comparing two compound distributions each with componentsf1(x) andf2(x), and with mixing proportionspxand (1 –px) for the first, andpyand (I –py) for the second distribution, respectively. Four methods are proposed for testing the hypothesisHo:px=py. The first two tests are based on the asymptotic normality of two unbiased estimators forpy–px, and the other two are nonparametric tests. The asymptotic power functions for the tests are given and a simulation technique is used to compare the efficiencies of the four tests applied for mixed normal and for mixed exponential distributions.