Data were obtained on 10,729 homicides that occurred in Chicago between 1975 and 1995. The victim-offender relationship was analyzed according to three categories--intimates, acquaintances, and strangers. Motive was coded in the analysis as expressive or instrumental, and several dummy-coded demographic characteristics of both victims and offenders were assessed to determine their potential independent effects on the likelihood of deviant homicides. Results of logistic regression analysis supported the hypothesis that the likelihood of deviant circumstances was significantly greater when homicides involved Hispanics, blacks, and males. In addition, deviant homicides were significantly more likely when they involved gang circumstances and, on the national level, after the appearance of crack cocaine. The findings have important implications for the explanatory power of criminological theory. The authors recommend further research to study homicide events in more meaningful disaggregations. The variable coding schemes used in the analysis are included in an appendix. 43 references, 7 notes, 4 tables, and 1 figure