The theory of spin-wave interactions is discussed using the double-time temperature-dependent Green's function technique. It is shown how the important parts of the third-order Green's functions can be deduced rigorously. By neglecting the remaining parts of these third-order functions it is then possible to obtain closed expressions for the first-order Green's functions and the spin correlation functions. One further approximation, which however is rigorous in the two limits S = 12 and S = ∞, is used. In agreement with Dyson's spin-wave theory it is found that ‘kinematic’ interactions produce no effects on the magnetization at low temperatures. However, it is shown that the kinematic interactions do affect the neutron cross sections for creation or annihalation of spin waves and the transverse magnetic susceptibility, and therefore, may be observed directly.