The problem of assessing chemical interactions in studies of genotoxicity is discussed. Attention is focused on assessing possible synergism or potentiation when the observed genotoxic response is binary (yes-no). Different forms of enhancement are distinguished based upon different assumptions on the genotoxic activity of the experimental treatments. A generalized linear statistical model is considered that links the probability of the binary response to the doses, and data-analytic strategies are described for detecting synergy and potentiation in factorially designed experiments. This approach is illustrated with a series of analyses of various genotoxicity data-sets.