Relative-rate tests have previously been developed to compare the substitution rates of two sequences or two groups of sequences. These tests usually assume that the process of nucleotide substitution is stationary and the same for all lineages, i.e., uniform. In this study, we conducted simulations to assess the performance of the relative-rate tests when the molecular-clock (MC) hypothesis is true (i.e., there is no rate difference between lineages), but the stationarity and uniformity assumptions are violated. Kimura's and bias-corrected LogDet distances were used. We found that the computation of the variances and covariances of LogDet distances had to be modified, because the constraint that the sum of the frequencies of the 16 nucleotide pair types is equal to 1 must be imposed. Comparison of the rates of two single sequences (Wu and Li's test) or two groups of sequences (Li and Bousquet's test) gave similar results. When the sequences are long (> or = 500 nt), the test based on LogDet distances and their appropriate variances and covariances is appropriate even when the substitution process is not stationary and/or not uniform. That is, at the 5% significance level, the test rejects the MC hypothesis in about 5% of the simulation replicates. In contrast, if the sequences are short (< or = 200 bases) and highly divergent, the LogDet test is very conservative due to overestimation of the variances of the distances. When the uniformity assumption is violated, the relative-rate test based on Kimura's distances can be severely misleading because of differences in base composition between sequences. However, if the uniformity assumption held and so the base frequencies remained similar among sequences, the rate of rejection turned out to be close to 5%, especially with short sequences. Under such conditions, the test using Kimura's distances performs better than the LogDet test. The reason seems to be that these distances are less affected by a reduction in the number of sites than the LogDet distances because they depend on only two parameters.