Instability of the excitation spectrum of an ordered noncollinear Heisenberg antiferromagnet with respect to spontaneous two-magnon decays is investigated. We use a spin-1/2 antiferromagnet on a triangular lattice as an example and examine the characteristic long- and short-wavelength features of its zero-temperature spectrum within the 1/S approximation. The kinematic conditions are shown to be crucial for the existence of decays and for overall properties of the spectrum. The XXZ and the J-J generalizations of the model, as well as the role of higher-order corrections, are discussed.
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