The excitation of first‐order spin‐wave instabilities in an antiferromagnet which may carry a nuclear moment is reexamined. Nuclear, electronic, and mixed magnon pairs can be excited by processes which are analogous to the ferromagnetic case. Various geometries of pumping fields are possible and their critical values are given. Contrary to the assumption of previous authors, we show that when photon pumping fields are applied to a flopped antiferromagnet, the uniform precessionis always excited, and its contribution to the threshold amplitude is significant andcan never be neglected. This implies that direct magnon excitation in which the linear susceptibility is negligibly small (parallel pumping) does not exist in an antiferromagnet when the weak dipolar effects are ignored. However, when phonon fields are applied, parallel pumping processes are allowed due to the change in symmetry of the effective magnetoelastic pumping field. In particular when a longitudinal wave is propagating parallel (or nearly so) to the dc sublattice magnetizations the effect of the negligibly small linear subsceptibility can be ignored and the process is analogous to parallel pumping in a ferromagnet.