The performance of analysis of covariance (ANCOVA) and six selected competitors was examined under varying experimental conditions through Monte Carlo simulations. The six alternatives were: (1) Quade's procedure (D. Quade, 1967); (2) Puri and Sen's solution (M. Puri and P. Sen, 1969); (3) Burnett and Barr's rank difference scores (T. Burnett and D. Barr, 1977); (4) Conover and Iman's rank transformation test (W. Conover and R. Iman, 1982); (5) Hettmansperger's procedure (T. Hettmansperger, 1984); and (6) the Puri-Sen-Harwell-Serlin test (R. Harwell and R. Serlin, 198). The conditions that were manipulated included assumptions of normality and variance homogeneity, sample size, number of treatment groups, strength of the covariate/dependent variable relationship, and multiple combinations of these factors. Results indicate that variance heterogeneity, especially in combination with unbalanced designs and severe nonnormality, had a profound impact on Type I error rates. The ANCOVA F-test was robust and exhibited high power under variance homogeneity, and for some cases of variance heterogeneity, but became less competitive as conditions departed from normality. (Contains 4 tables and 23 references.) (SLD)