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abstract: 'Zero-field specific heat of the single crystals $R$Ni$_{2}$B$_{2}$C ($R$= Er, Ho, Dy, Tb, Gd) was measured within the temperature range 0.1 K$<T<$25 K.  Linearized spin wave analysis was successfully applied to account for and to rationalize the thermal evolution of the low–temperature magnetic specific heats of all the studied compounds (as well as the one reported for TmNi$_{2}$B$_{2}$C) in terms of only two parameters, namely an energy gap $\Delta$ and a characteristic temperature $\theta$. The evolution of $\theta$ and $\Delta$ across the studied compounds correlates very well with the known magnetic properties. $\theta,$ as a measure of the effective $RKKY$ exchange couplings, scales reasonably well with the de Gennes factor. $\Delta,$ on the other hand, reflects predominately the anisotropic properties: $\sim2$ K for GdNi$_{2}$B$_{2}$C, $\sim6$ K for ErNi$_{2}$B$_{2}$C, $\sim7$ K for TbNi$_{2}$B$_{2}$C, and $\sim8$ K for each of HoNi$_{2}$B$_{2}$C and DyNi$_{2}$B$_{2}$C. The equality in $\Delta$ 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$_{1-x}$Ni$_{2}$B$_{2}$C ($x<0.8$ and $T_{c}<T_{N}$) would not lead to any softening of $\Delta$. This supports the hypothesis of Cho et al (PRL **77**,163(1996)) concerning the influence of the collective magnetic excitations on 