  The electronic Raman response in the electron-doped cuprate superconductors
is studied based on the $t$-$t'$-$J$ model. It is shown that although the
domelike shape of the doping dependent peak energy in the $B_{2g}$ symmetry is
a common feature for both electron-doped and hole-doped cuprate
superconductors, there are pronounced deviations from a cubic response in the
$B_{1g}$ channel and a linear response in the $B_{2g}$ channel for the
electron-doped case in the low energy limit. It is also shown that these
pronounced deviations are mainly caused by a nonmonotonic d-wave gap in the
electron-doped cuprate superconductors.
