  We study the emergence of a magnetic resonance in the superconducting state
of the electron-doped cuprate superconductors. We show that the recently
observed resonance peak in the electron-doped superconductor
Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$ is consistent with an overdamped spin
exciton located near the particle-hole continuum. We present predictions for
the magnetic-field dependence of the resonance mode as well as its temperature
evolution in those parts of the phase diagram where $d_{x^2-y^2}$-wave
superconductivity may coexist with an antiferromagnetic spin-density wave.
