  We investigate magnetic excitations in the $S=1$ easy-plan-type triangular
antiferromagnets CsFeCl$_{3}$ and RbFeCl$_{3}$ through a combination of
inelastic neutron scattering measurements and spin-wave theory calculations
based on an established exchange-coupling Hamiltonian. We show that in either
material the model falls short of providing an adequate description of the
measured intensities and for RbFeCl$_{3}$ even fails to reproduce the measured
dispersion relation. The most striking discrepancy is a very anisotropic
azimuthal intensity distribution in the acoustic spin-wave branches in the
long-wavelength limit, which is incompatible with spin-wave theory on a
fundamental level. The observed anomalies are attributed to long-range dipolar
interactions.
