This paper presents a discussion about a spin model arising out of singleand double-electron exchange processes. The Hamiltonian which consists of the usual Heisenberg exchange, biquadratic exchange and three-atom coupling is studied using the Green function equation-of-motion method within the random-phase approximation. The effects of biquadratic exchange and three-atom coupling on the magnetization curves, quadrupolar ordering and the transition temperature T_C are studied. It is shown that the magnetization changes from second to first order at T_C depending on the strengths of the biquadratic and three-atom coupling. It is also seen that T_C becomes equal to zero at certain values of the parameters. The results are compared with those of molecular-field theory.