In a previous paper we have discussed how the Landau potential (entering in
Landau theory of phase transitions) can be simplified using the Poincar\'e
normalization procedure. Here we apply this approach to the Landau-deGennes
functional for the isotropic-nematic transitions, and transitions between
different nematic phases, in liquid crystals. {We give special attention to
applying our method in the region near the main transition point, showing in
full detail how this can be done via a suitable simple modification of our
Poincar\'e-like method. We also consider the question if biaxial phases can
branch directly off the fully symmetric state; some partial results in this
direction are presented
