A kinetic theory of spectral band shapes is developed which accounts for the effects of line mixing and finite duration of collisions. The theory is based on a projection operator technique with a nonorthogonal metric. The roles and hierarchy of various approximations commonly employed are analyzed. It is shown that the relaxation operator must be defined before the initial correlations are suppressed so that the double sum rule for the matrix elements of this operator is conserved. This conservation is important for the calculations of the wings of band shapes. Rotovibrational band shapes for some specific cases of Raman and infrared absorption spectra of gases are considered. The expressions obtained relate the band wing profiles with the spectral density of molecular torque arising from binary collisions. (C) 1998 American Institute of Physics.