A sample of 6188 nearby galaxy structures, complete to r_F = 183 and containing at least 10 members each, was the observational basis for an investigation of the alignment of bright galaxies with the major axes for the parent clusters. The distribution of position angles for galaxies within the clusters, specifically the brightest, the second brightest, the third, and the tenth brightest galaxies was tested for isotropy. Galaxy position angles appear to be distributed isotropically, as are the distributions of underlying cluster structure position angles. The characterization of galaxy structures according to richness class also appears to be isotropic. Characterization according to BM types, which are known for 1056 clusters, is more interesting. Only in the case of clusters of BM type I is there an alignment of the brightest cluster member with the major axis of the parent cluster. The effect is observed at the 2 significance level. In other investigated cases the distributions are isotropic. The results confirm the special role of cD galaxies in the origin/evolution of large-scale structures.