Abstract
A generalized mean field approximation is used to find sufficient conditions for the existence of stable quadrupole phases in spin systems with atomic spin s and described by isotropic nearest-neighbour bilinear and biquadratic exchange. Quadrupolar phases are defined as having thermal averages such that (si.ii)0=0 while ((si.ui)2)0 has a value different than its paramagnetic value, ui is a unit vector at site i in the direction of the local mean field. By determining the ui variationally, phases not previously discussed are found.