Abstract The non-Debye reorientation processes in which the Debye equation is inapplicable are studied for spherical molecules by using an equation proposed by the author. The physical meaning of the angular correlation in the non-Debye processes is discussed in detail. It is shown that in the non-Debye processes the non-dissipative decay of the mutual-phase correlation of rotating molecules must be taken into account, in addition to the dissipative decay due to molecular collisions, and that the use of the “microscopic viscosity” in the Debye equation is not plausible. It is also shown that, in contrast to the Debye processes, there is no one-to-one correspondence between the correlation time for molecular reorienation and the mean life time of the rotation, since the contribution from the nondissipative decay should be considered also. The vector and the tensor correlation functions, 〈cosθ(0)cosθ(t)〉 and 〈(1⁄2){3cos2θ(0)−1}{(1⁄2)3cos2θ(t)−1}〉, and the corresponding spectral densities, the band shapes of infrared and Raman spectra respectively, are obtained theoretically for various conditions and are shown graphically. As illustravtie examples of the treatment, methane and deutero methane molecules are studied. Vector correlation functions are obtained from the observed band shapes of the infrared spectra of these molecules. Comparing the theoretical correlation functions with experimental ones, it is shown that a reasonable agreement between theory and experiment is obtained and that methane molecules have a typical non-Debye reorientation process even below the freezing point. Some characteristic features of the non-Debye process are also discussed.