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The U.S. EPA must provide guidance as to health risk assessment of mixtures from a variety of sources such as wastewaters, hazardous waste sites and air particulates. One approach to risk assessment of mixtures is to add up risk assessments for individual components identified as part of the mixture, after considering the potential for interaction among those components. This provides an index of hazard potential but not a quantitative estimate. When data on mixture components are incomplete, but these components are isomers or congeners of a well-studied chemical, another technique--use of toxic equivalency factors--can be applied. This approach has been proposed for estimating risk associated with chlorinated dioxins and dibenzofurans. A third approach, that of relative or comparative potency, is based on the assumption that for similar but not necessarily definable complex mixtures, a measure of relative potency based on data from in vitro tests can be correlated in a constant fashion with relative potency from an in vivo bioassay. The degree of confidence in the appropriateness of a relative potency method rests upon the way potency is measured and the validity of underlying assumptions (the degree to which these assumptions can be tested). One class of assumptions involves choice of the model or procedure for deriving the quantitative risk estimates. A second set of assumptions deals with mechanism of action, and whether such considerations add bias or, in fact, refine the relative potency judgment. The choice of short-term tests appropriate for use in establishing the potency relationships is also a factor to be considered. This paper presents examples of proposed uses of relative potency in risk assessment and outlines some areas for further study.