  We study the kinetics of spin coherence of optically excited electrons in an
undoped insulating ZnSe/Zn$_{1-x}$Cd$_x$Se quantum well under moderate magnetic
fields in the Voigt configuration. After clarifying the optical coherence and
the spin coherence, we build the kinetic Bloch equations and calculate
dephasing and relaxation kinetics of laser pulse excited plasma due to
statically screened Coulomb scattering and electron hole spin exchange. We find
that the Coulomb scattering can not cause the spin dephasing, and that the
electron-hole spin exchange is the main mechanism of the spin decoherence.
Moreover the beat frequency in the Faraday rotation angle is determined mainly
by the Zeeman splitting, red shifted by the Coulomb scattering and the electron
hole spin exchange. Our numerical results are in agreement with experiment
findings. A possible scenario for the contribution of electron-hole spin
exchange to the spin dephasing of the $n$-doped material is also proposed.
