  We investigate the generalized p-spin models that contain arbitrary diagonal
operators U with no reflection symmetry. We derive general equations that give
an opportunity to uncover the behavior of the system near the glass transition
at different (continuous) p. The quadrupole glass with J=1 is considered as an
illustrating example. It is shown that the crossover from continuous to
discontinuous glass transition to one-step replica breaking solution takes
place at p=3.3 for this model. For p <2+\Delta p, where \Delta p= 0.5 is a
finite value, stable 1RSB-solution disappears. This behaviour is strongly
different from that of the p-spin Ising glass model.
