We present results from a ROSAT HRI study of 11 distant (z~0.2-0.3) Abell clusters. We have performed a morphological analysis to search for and quantify substructure in the clusters. About 70 per cent of the sample shows significant evidence of substructure in the form of centroid shift or obvious X-ray clumps. We examine the clusters for the presence of cooling flows, and determine the physical properties of the ICM by deprojecting the HRI data. Nine of the clusters have central cooling times less than the age of the system, in agreement with fractions determined from nearby, X-ray-bright samples. Additional PSPC results are presented for four clusters in the sample, and ASCA results for six clusters. The temperatures and metallicities for these distant clusters appear to be consistent with nearby clusters of similar richness.