First-principles calculations of the electronic structure of members of the $R$NiC$_2$ series are presented, and their Fermi surfaces investigated for nesting propensities which might be linked to the charge-density waves exhibited by certain members
of the series ($R$ = Sm, Gd and Nd). Calculations of the generalized susceptibility, $chi_{0}({bf q},omega)$, show strong peaks at the same ${bf q}$-vector in both the real and imaginary parts for these compounds. Moreover, this peak occurs at a wavevector which is very close to that experimentally observed in SmNiC$_2$. In contrast, for LaNiC$_2$ (which is a superconductor below 2.7K) as well as for ferromagnetic SmNiC$_2$, there is no such sharp peak. This could explain the absence of a charge-density wave transition in the former, and the destruction of the charge-density wave that has been observed to accompany the onset of ferromagnetic order in the latter.
