The motion of cosmic rays in interplanetary space as determined by observed magnetic-field power spectra is discussed in detail, extending the analysis in an earlier paper. The assumptions of statistical homogeneity and isotropy of the magnetic fluctuations are critically examined, and the conditions under which diffusion adequately describes the particle motion are defined. It is concluded that the small cyclotron radius limit is applicable to particles less than a few GeV energy. From the reported power spectra, it is concluded that the motions of cosmic rays with kinetic energies between about 10 MeV/ nucleon and a few GeV/nucleon are well represented by diffusion with a diffusion tensor proportional to Rp, where R is the particle magnetic rigidity and cp is its velocity. The parallel diffusion coefficient l has a value 2 X 10ii for 100 MeV protons, whereas the perpendicular component is much smaller. Parker's model for the long-term modulation of galactic cosmic rays, including adiabatic deceleration, is generalized to include an energy dependent diffusion coefficient. The predictions of this model, with Rp, are consistent with the observed long-term variations and radical gradient of galactic cosmic rays during the period approaching solar minimum. This is in agreement with earlier conclusions based on the simple diffusion-convection model, neglecting adiabatic deceleration. However, a definitive test of this general picture awaits more detailed and simultaneous measurements of cosmic rays and the interplanetary magnetic-field irregularities. In particular it is found that the quantitative predictions of the model may depend in a significant manner on the heliocentric radial variation of `c.