  Various models of structure formation can account for various aspects of the
galaxy formation process on different scales, as well as for various
observational features of structures. Thus, the investigation of galaxies
orientation constitute a standard test of galaxies formation scenarios since
observed variations in angular momentum represent fundamental constraints for
any model of galaxy formation. We have improved the method of analysis of the
alignment of galaxies in clusters. Now, the method allowed analysis both
position angles of galaxy major axes and two angles describing the spatial
orientation of galaxies. The distributions of analyzed angles were tested for
isotropy by applying different statistical tests. For sample of analyzed
clusters we have computed the mean values of analyzed statistics, checking
whether they are the same as expected ones in the case of random distribution
of analyzed angles. The detailed discussion of this method has been performed.
We have shown how to proceed in many particular cases in order to improve the
statistical reasoning when analyzing the distribution of the angles in the
observational data. Separately, we have compared these new results with those
obtained from numerical simulations. We show the powerful of our method on the
example of galaxy orientation analysis in 247 Abell rich galaxy clusters. We
have found that the orientations of galaxies in analyzed clusters are not
random. It means that we genuinely confirmed an existence of the alignment of
galaxies in rich Abells' galaxy clusters. This result is independent from the
clusters of Bautz-Morgan types.
