The purpose of this paper is the study of the dipole and quadrupole anisotropy brightness arising from the motion of the observer in the presence of a pure Planckian spectrum and in the case of a submillimeter excess. We find that the dipole anisotropy is enhanced in the case of the excess measured by the Japanese-USA groups, while it is decreased in the case of the excess found by the Candian group. The quadrupole term is absent in the radio region, while it acquires detectable values in the infrared. Comparisons are made with the observational values, and the possibility of observing the quadrupole pattern in the presence of galactic dust contamination is discussed.