We investigate longitudinal and transverse uniaxial and biaxial fluctuations in nematic liquid crystals. We show that the director fluctuations make a singular contribution not only to the longitudinal but also to the biaxial fluctuations. A general expression is constructed in the Gaussian approximation for the fluctuating contribution of the tensor order parameter to the thermodynamic potential of the liquid crystal. When account is taken of the spatial dispersion in the approximation quadratic in the wave vector, this expression contains twelve independent coefficients. In particular, for the difference K,, - K,, of the Frank moduli it predicts a cubic dependence on the order parameter. The correlation function of the orientation fluctuation is calculated for both the nematic and the isotropic phase. A general analysis is presented of the conditions for the observation longitudinal and biaxial fluctuations in the usual light-scattering experimental geometry