Tunneling spectra of a single crystalline YNi2B2C (T-c = 15.4 K) and L
uNi2B2C (T-c = 15.7 K) have been measured by a point-contact spectrosc
opy using a low-temperature scanning tunneling microscope. The conduct
ance curve of these materials shows a smeared gap structure with an al
most linear density of states inside of the gap region as well as a si
zable zero-bias conductance. The linear conductance inside the gap reg
ion has been explained by a proximity-induced energy gap in the degrad
ed surface normal layer. The resulting energy gap at 4.2 K is 3.2 meV
and 3.3 meV for YNi2B2C and LuNi2B2C, respectively. A simple analysis
using a smeared BCS density of states, on the other hand, yields energ
y gap of 2.55 meV and 2.65 meV. Temperature dependence of the energy g
ap in LuNi2B2C shows a reasonable agreement with the BCS type temperat
ure dependence except a slight deviation near T-c.