The observable anisotropy of cosmic rays has first been decomposed into zonal harmonics and components of vector and tensor anisotropy. We examine Forbush decreases in cosmic rays that occurred in November 2001 and November 2004. It is shown that at the beginning of a Forbush decrease an antisunward convective current of cosmic rays predominates; and during the recovery phase, a sunward diffusive current of particles along the interplanetary magnetic field dominates. During the phase of intensity drop, short-time decreases in the second zonal harmonic take place. These decreases occur with abrupt changes of the interplanetary magnetic field intensity and solar wind speed. During the passage of large-scale solar wind disturbances, the tensor anisotropy behaves in a complicated way. To explain its behavior, a further detailed investigation is required.