  By an electrical-pump--optical-probe technique we show that the
electric-field-induced reversal of the magnetic order parameter in multiferroic
MnWO$_4$ occurs on the time scale of milliseconds and maintains a rigid
coupling of the magnetization to the magnetically induced electric
polarization. The temporal progression of the spatially resolved domain
structure was imaged with nanosecond resolution by optical second harmonic
generation and compared to the quasi-static domain reversal. A qualitative
model gives an estimate of why the magnetoelectric order-parameter reversal in
the magnetically induced ferroelectrics is not inherently ultrafast.
