  We argue that the experimentally observed nonmonotonic gap in electron-doped
cuprates at optimal doping is the lowest quasiparticle excitation energy in the
coexisting antiferromagnetic (AF) and superconducting (SC) state. The idea is
implemented by studying the coexistence of AF and SC orders with the t-t'-t''-J
model. Although the pairing gap itself is assumed to be the simplest $d$ wave
which is monotonic, we have found that the quasiparticle excitation gap in the
coexisting state is nonmonotonic, with the maxima around the hot spots where
the Fermi surface is missing due to the AF gap. Within the same framework of
the coexisting state the spectral function is also calculated at optimal
doping. The obtained results are all consistent with experiments.
