The integrodifferential equation governing the time behaviour of the longitudinal spin relaxation function in the high-temperature approximation is studied. The analysis clarifies the consistency of possible approximations to the kernel with the asymptotic behaviour of the solution. It is found that the presence or absence of exchange interaction leads to completely different behaviours in the coupling constant λ. Correspondingly different approximation schemes are allowed. An expression for the solution, of rather general validity, is given. This expression is correct up to terms of second order in the coupling constant and is obtained directly by quadrature on the kernel.