We have studied in the molecular field approximation the statistical mechanical properties of the Hamiltonian H= ∑ mnJ(m−n)Sm·Sn− ∑ mnj(m−n)(Sm·Sn)2,for spin one ions. Other authors have already shown that the biquadratic term can cause the magnetic transition to become first order.1 Closer examination shows that one must consider, in addition to the usual long-range order parameter 〈Sz〉=M, the possibility of ``quadrupolar'' ordering in the independent parameter Q=〈Sz2〉−23. If the biquadratic exchange is sufficiently large the quadrupolar ordering will appear at a temperature TQ which is different from that at which dipolar ordering M appears, so that two separate phase transitions are found. The phase diagram is discussed as a function of the ratio of bilinear to biquadratic exchange, and the interplay between quadrupolar and dipolar ordering is considered.