We have found that there is a significant difference in the rigidity dependence of the 11-year variation of the galactic cosmic rays in the rigidity interval from 0.6 to 100 GV between the A>0 modulation cycle from 1977 to 1981 and the A<0 cycle from 1987 to 1990. The overall intensity decrease from 1977--1981 is found to have a rigidity dependence given by F(P)=exp(-1.46¿P-1.22¿0.05), where F(P) is the modulation function and P is the rigidity [GV> and for 1987--1990 F(P)=exp(-1.75¿P-1.02¿0.05). For the conventional diffusion-convection theory of modulation the rigidity dependence of the modulation is equal to the rigidity dependence of the interplanetary diffusion coefficient. For a selected number of Forbush decreases we found that the rigidity dependence of the decreases occurring near the period of minimum solar modulation was steeper than for those occurring later in the solar cycle. In no case was the rigidity dependence of any transient decrease much different from that of the 11-year variation, however. The crossover in the 1977 and 1987 primary proton energy spectra at E~400 MeV observed near sunspot minimum shifts to ~650 MeV at the time of the maximum solar activity or minimum cosmic ray intensity. ¿ American Geophysical Union 1996