Analytical expressions for the elastic constants of nematic polymer solutions are derived when the macromolecules are monodisperse rod-like, bidisperse rodlike or semi-flexible. These expressions are derived in the gaussian approximation so that they constitute exact leading terms of a general asymptotic expansion for high degree of nematic ordering although the results are justifiable only within the range of validity of the second virial approximation. The limiting forms are in complete agreement with recent numerical work for monodisperse rods.