The theory of dielectric relaxation of uniaxial nematic liquid crystals is developed without recourse to the Fokker–Planck equation by direct averaging of the non-inertial Langevin equation for the rotational brownian motion of the linear molecule in a mean-field nematic potential. The non-inertial equation is regarded as a non-linear Stratonovich stochastic differential equation. The molecular equations for the average values of the dipole moment components so obtained involve both the nematic field and a suddenly applied weak DC measuring field. The equations are linearized in the DC field so that the AC response may be found by linear response theory. The Laplace transform of the equations is closed by a procedure which corresponds exactly to the effective eigenvalue method. It allows one to obtain formulae valid for all barrier heights for the longitudinal τ ∥ and transverse τ ⊥ relaxation times for an arbitrary uniaxial nematic potential in terms of the order parameter. The complex susceptibility induced by a weak AC field applied parallel and perpendicular to the axis of symmetry is also calculated.