The toxic equivalency factor (TEF) method has been used to characterize the toxicity of human mixtures of dioxin-like compounds and is being considered for use with other classes of potentially toxic agents. TEFs are estimated by examining the relative potencies of the various congeners for a series of biological and toxicological effects. In this paper, we consider changes in activity for two enzymes, cytochrome P450 1A1 (CYP1A1)-associated 7-ethoxyresorufin-O-deethylase (EROD) and CYP1A2-associated acetanilide-4-hydroxylase (A4H) activity, resulting from exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), 3,3',4,4',5-pentachlorobiphenyl (PCB), 2,3,4,7,8-pentachlorodibenzofuran (PeCDF) or a mixture of these agents. The ratio of median effective dose (ED 5 0 ) is one way to estimate the relative potencies, especially for gene expression and protein endpoints. ED 5 0 's were estimated with a nonlinear regression model in which dose-related changes in mean responses are described by a Hill function. ED 5 0 's along with other model parameters were estimated by fitting this model to a given data set. Significant differences in estimated model parameters were tested by likelihood ratio methods. The estimated parameters indicated that congener-specific dose-response shapes were significantly different, that additivity failed for these congeners, and that the ratios of ED 5 0 's did not predict the response seen for the mixture. These results indicate that for some biological responses, the use of a single relative potency factor (RPF) is not appropriate for the comparison of the dose response behavior of different dioxin-like congeners.