Simple formulae which yield a close approximation to the exact analytic solution for the longitudinal and transverse relaxation times T parallel to and T perpendicular to of the components of the dipole moment of a nematic liquid crystal with simple uniaxial anisotropy are presented. The new formula for T parallel to yields a substantial correction to the Meier-Saupe formula [1966, Molec. Crystals, 1, 515]. It appears that both the longitudinal and transverse relaxation processes may be accurately described by a single Debye type relaxation mechanism with relaxation times T parallel to and T perpendicular to.