The paper considers the problem of performing all pairwise comparisons of means ineach row of a two-way ANOVA. This problem arises in situations where an investigator is concerned about disordinal interactions. For the equal variance case the proposed procedure is based on an extension of Tukey's procedure. The new procedure requires percentage points of the “multivariate” Studentized range distribution, and a table of these percentage points is provided. For unequal variances, extensions of the Games and Howell (1976) technique as well as Dunnett's (1980) T3 and C procedures can be used. Simulation results suggest that these latter procedures perform in a manner similar to the situations studied by Dunnett. In particular, the extension of Dunnett's T3 procedure appears to be best, among the procedures studied, when the degrees of freedom areless than 50 for any treatment group. Otherwise, use the extension of Dunnetts C.