The toxicity of polychlorodibenzofurans (PCDFs), produced during incineration and in accidental fires involving polychlorinated biphenyls (PCBs), is generally assessed in terms of total concentration or more recently in terms of the group concentrations of the tetra-, penta- and hexachloro-isomers. This approach fails to account for the great differences in potency of the relatively few toxic congeners and isomers present in the sample. A quantitative risk assessment of PCDF mixtures must not only be based on the concentrations of the toxic components but also account for the relative potency of each congener in a form which permits summation of the toxicities of the individual contributors. This paper outlines a method by which the concentration of each of the toxic components, determined by high-resolution congener-specific gas chromatographic analysis, may be converted to equivalent toxic concentrations of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). Summation of the resulting values permits the overall toxicity of the sample to be expressed in terms of an equivalent toxic weight of TCDD per unit weight of sample (ng TCDD/g) in the case of fly ash or an equivalent toxic weight of TCDD per unit area (ng TCDD/m2) for soot deposit.