SummaryA Monte Carlo study of the size and power of tests of equality of two covariance matrices is carried out. Tests based upon normality assumptions, elliptical distribution assumptions as well as distribution‐free tests are compared. Samples are generated from normal, elliptical and non‐elliptical populations. The elliptical‐theory tests, in particular, have poor size properties for both elliptical distributions with moderate sample sizes and for non‐elliptical distri