Summary
    Complementary one-, two- and three-dimensional tests for detecting the presence of substructure in clusters of galaxies are applied to recently obtained data from the 2dF Galaxy Redshift Survey. The sample of 25 clusters used in this study includes 16 clusters not previously investigated for substructure. Substructure is detected at or greater than the 99 per cent confidence level in at least one test for 21 of the 25 clusters studied here. From the results, it appears that low-richness clusters commonly contain subclusters participating in mergers. About half of the clusters have two or more components within 0.5 h−1 Mpc of the cluster centroid, and at least three clusters (Abell 1139, Abell 1663 and Abell S333) exhibit velocity-position characteristics consistent with the presence of possible cluster rotation, shear, or infall dynamics. The geometry of certain features is consistent with influence by the host supercluster environments. In general, our results support the hypothesis that low-richness clusters relax to structureless equilibrium states on very long dynamical time-scales (if at all)