Zero-field specific heats of the single crystals RNi 2 B 2 C (RϭEr, Ho, Dy, Tb, Gd͒ were measured within the temperature range 0.1 KϽTϽ25 K. Linearized spin-wave analysis was successfully applied to account for and to rationalize the thermal evolution of the low-temperature magnetic specific heats of all the studied compounds ͑as well as the one reported for TmNi 2 B 2 C) in terms of only two parameters, namely, an energy gap ⌬ and a characteristic temperature . The evolution of and ⌬ across the studied compounds correlates very well with the known magnetic properties. , as a measure of the effective Ruderman-Kittel-Kasuya-Yosida exchange couplings, scales reasonably well with the de Gennes factor. ⌬, on the other hand, reflects predominately the anisotropic properties: ϳ2 K for GdNi 2 B 2 C, ϳ6 K for ErNi 2 B 2 C, ϳ7 K for TbNi 2 B 2 C, and ϳ8 K for each of HoNi 2 B 2 C and DyNi 2 B 2 C. The equality in ⌬ of HoNi 2 B 2 C and DyNi 2 B 2 C, coupled with the similarity in their magnetic configurations, indicates that a variation of x in the solid solution Ho x Dy 1Ϫx Ni 2 B 2 C (xϽ0.8 and T c ϽT N ) would not lead to any softening of ⌬. This supports the hypothesis of Cho et al. ͑Ref. 35͒ concerning the influence of the collective magnetic excitations on the superconducting state. This work underlines the importance of spin-wave excitations for a valid description of low-temperature thermodynamics of borocarbides.