Stability of Type I error rates and power are investigated for three forms of the Box test and two forms of the jackknife test with equal and unequal sample sizes under conditions of normality and nonnormality. The Box test is shown to be robust to violations of the assumption of normality when sampling is from leptokurtic populations. The jackknife test is not robust. When n's are unequal, previously reported suggestions for selecting subsample sizes for the Box test are shown to be inappropriate, producing a permissive test. The problem of heterogeneous within cell variance and unequal n's is discussed. Two procedures which alleviate this problem are presented for the Box test. Use of the jackknife test with a reduced alpha is shown to provide power and control of Type I error at approximately the same level as the Box test. (Author)