It is shown theoretically that, for non-Kramers paramagnetic ions, the second-order Raman phonon process gives a spin–lattice relaxation rate varying as T5 at low temperatures. This new relaxation rate for non-Kramers ions is similar to the one discussed by Orbach and Blume for multilevel Kramers ions. An unusual feature of the second-order Raman process as applied to non-Kramers doublets is that terms in the spin–lattice interaction which are diagonal in the spin states enter in an essential way. The conditions under which the T5 relaxation process dominates other relaxation processes are discussed.