An analysis is presented for a statistically complete sample of 547 galaxy structures with z ≤ 0.16, each containing at least 10 objects. The sample was divided according to structure richness, representing 10 richness classes, with the distribution of ellipticities differing among individual classes. Mean ellipticity varies from 0.34 to 0.18, less well populated structures being more elongated that richer ones. Statistics indicate that structures with at least 50 members originate from the same population. The mean redshift of a structure class is a function of richness, with less well populated classes exhibiting greater mean redshifts than richer galaxy clusters. Further analysis reveals a dependence of the ellipticity-redshift correlation on structure richness. Among rich galaxy clusters there is an anti-correlation between the parameters, the strongest correlation occurring for the most poorly populated galaxy classes.