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Uniaxial magnets with spin one, single-ion anisotropy, and anisotropic biquadratic exchange interaction are investigated in the absence of magnetic field. Possible types of quadrupole ordering in the system are discussed for the case in which the anisotropy of biquadratic exchange interaction has the most general form compatible with the axial symmetry. Besides the two phases with the stationary planes of quadrupole ordering (QOZ and QOX phases), there may appear a phase (QO< phase) in which the orientation of the quadrupolar-ordering plane changes continuously as the Hamiltonian parameters are varied. For the QOX phase, two branches of spin excitations have been found, one of which includes the Goldstone mode. The QO< phase boundary with the other two quadrupolar phases at finite temperatures has been determined, the expression for the QO<–QOZ phase boundary has been derived analytically.

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