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The field dependence of spectrum of nuclear spin waves is investigated in a uniaxial antiferromagnet. With the increase of external magnetic field H_0//c-axis, a continuous transition from single-spin to collective excitation behavior is found. In particular, the dispersion of nuclear spin waves appears remarkably for small values of wave vector κ in the immediate vicinity of H_, the spin-flop field. The frequency of uniform modes is also calculated as a function of field. Qualitative agreement between observations and theory is obtained