We present a phenomenological theory for the homogeneous phases of nematic liquid crystals constituted by biaxial D(2h)-symmetric molecules. We propose a general polynomial free-energy in two macroscopic order tensors that reproduces the mean-field phase diagram confirmed by Monte Carlo simulations [De Matteis et al., Phys. Rev. E 72, 041706, (2005)] and recently recognized to be universal [Bisi et al., Phys. Rev. E 73, 051709, (2006)] for dispersion forces molecular pair potentials enjoying the D(2h) symmetry. The requirement that the phenomenological theory comply uniquely with this phase diagram reduces considerably the admissible phenomenological coefficients, both in their number and in the ranges where they can vary. We also consider a generalization of the polynomial theory in order to describe non-homogeneous phases in confined geometries of liquid crystals.