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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 (ED50) is one way to estimate the relative potencies, especially for gene expression and protein endpoints. ED50's were estimated with a nonlinear regression model in which dose-related changes in mean responses are described by a Hill function. ED50'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 ED50'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.