The Dyson‐Maleev formalism is used to calculate the decay rate of antiferromagnetic spin waves at low temperatures and long wavelengths. Various regimes must be distinguished depending on the relation between the wavevector k, the temperature T, and the anisotropy energy. For the isotropic system the relevant parameters are (a) the incident energy, (b) the thermal energy, (c) the deviation from linearity ("curvature energy'') of thermal spin waves, and (d) the curvature energy of the incident spin wave. In the anisotropic case the damping of the k=0 mode has the same dependence on spin‐wave energy as in the isotropic system. In all cases, the decay rate is small compared to the frequency, which implies that the spin waves are appropriate elementary excitations for small k and T, and that they interact weakly among themselves in this limit. For k→0 with T fixed, the decay rate is proportional to k 2 in the isotropic system. This agrees with an earlier hydrodynamic prediction and contradicts previous microscopic calculations. In this low‐k limit the full spin‐spin correlation function is calculated, and it agrees with the hydrodynamic form proposed earlier. The possibility of experimental verification of these predictions is briefly discussed.