We deal with several-sample linear regressions in which the independent variables are assumed to be equispaced. It is assumed that one Y observation is available corresponding to each x. In this setting, we propose exactly distribution-free tests for the problem of testing the equality of intercepts (slopes) against the alternative that the intercepts (slopes) are in increasing (decreasing) order of magnitude. The proposed procedures are compared ( la PITMAN with the parametric theory counterparts.