  Recently a hybrid s+g-wave pairing is proposed to describe the experimental
observation for a nodal structure of the superconducting gap in borocarbide
YNi$_2$B$_2$C and possibly LuNi$_2$B$_2$C. In this paper the impurity effects
on the s+g-wave superconductivity are studied in both Born and unitarity limit.
The quasiparticle density of states and thermodynamics are calculated. It is
found that the nodal excitations in the clean system are immediately prohibited
by impurity scattering and a finite energy gap increases quickly with the
impurity scattering rate. This leads to an activated behavior in the
temperature dependence of the specific heat. Qualitative agreement with the
experimental results is shown. Comparison with d-wave and some anisotropic
s-wave studied previously is also made.
