This paper is concerned with the null distribution of the likelihood ratio test statistic − 2log Λ for testing the adequacy of a random-effects covariance structure in a parallel profile model. It is known that the null distribution of − 2log Λ converges to χ ² _f or 0 . 5 χ ² _f + 0 . 5 χ ² _{f +1} when the sample size tends to infinity. In order to extend this result, we derive asymptotic expansions of the null distribution of − 2log Λ. The accuracy of the approximations based on the limiting distribution and an asymptotic expansion are compared through numerical experiments.