Inelastic neutron scattering techniques have been used to study the low energy phonon excitations in superconducting RENi2B2C (RE=Lu, Y) to further characterize the anomalous features observed by Kawano et al. (Phys. Rev. Lett., 77, 4628 (1996)) for RE=Y and Stassis et al. (Phys. Rev. B, 55, R8678 (1997)) for RE=Lu, when these systems enter the superconducting ground state. We find that above T c the frequencies of the [delta]4[[xi] 00] lowest-lying acoustic and optic phonon modes decrease with decreasing temperature, for [xi] close to the nesting vector [xi]m. In addition there is a shift of intensity from the upper to the lower mode, an effect characteristic of mode coupling. At temperatures below approximately 100K only a single unresolved peak is observed. The observed anticrossing behavior of these modes above T c can be described satisfactorily in both compounds by a coupled-mode model. Below T c the observed spectrum changes dramatically: it consists of a sharp peak at approximately 4 meV with a broad weak shoulder at higher energies. The experimental results unambiguously show that this dramatic change is due to the onset of superconductivity in these compounds. In this temperature region, the results are in qualitative agreement with recent theoretical calculations.