We use some data of neutron monitors to calculate the average temporal changes of the rigidity spectrum of the galactic cosmic ray (GCR) intensity variations for the four ascending and four descending phases of solar activity (1960—2002) including the positive (A > 0) and negative (A < 0) polarity periods of solar magnetic cycles. The soft rigidity spectrum of the GCR intensity variations for the maximum epoch and the hard one for the minimum epoch obtained by the worldwide network of neutron monitors data are attributed by us to the essential rearrangement of the structure in the energy range of the interplanetary magnetic field (IMF) turbulence throughout the 11-year cycle of solar activity. There is not found any valuable regular difference between the changes of the rigidity spectrum of the 11-year variations of the GCR intensity for different A > 0 and A < 0 polarity epoch. We conclude that the rigidity spectrum exponent γ can be considered as one of the new indexes to study the 11-year variations of GCR intensity and to estimate the condition of the energy range of the IMF turbulence. The apparent 22-year (solar magnetic cycle) variations of the radial component of the GCR anisotropy caused by the drift due to the gradient and curvature of the regular IMF in different solar magnetic cycles were revealed by the neutron monitors data. A long period behaviour of the A_r component of the GCR anisotropy gives an opportunity to make a more reliable choice between the diffusion dominated or drift dominated models of GCR transport during the Sun’s global magnetic field reversal in the maxima epoch of solar activity.