An analysis is performed to ascertain the joint incidence of two causes of death, acute myocardial infarct and stroke, for the deaths of residents of Massachusetts and North Carolina in 1969. To assay their association an explicit biological model of the nature of the relation is posited. It is shown that, under this model, Chiang's (1968) theory of competing risks may be extended to the case in which an individual's death may have multiple causes. Furthermore, techniques are developed which allow us to model the survival parameters derived under the model by categorical data procedures of the type introduced by Grizzle, Starmer and Koch (1969). The study shows that there is a greater incidence of the joint occurrence of stroke and myocardial infarct on death certificates in North Carolina than in Massachusetts, a pattern consistent with the generally higher stroke mortality in North Carolina. Furthermore, the incidence of the joint occurrence of the two diseases shows a clear age "gradient" increasing through the age range of the analysis. Males and females show somewhat different patterns of age variation in that state-by-age interaction terms are more prominent in the model fitted for females than for males.