  We evaluate the width of the $\omega$ meson in nuclear matter. We consider
the free decay mode of the $\omega$ into three pions, which is dominated by
$\rho \pi$ decay, and replace the $\rho$ and $\pi$ propagators by their medium
modified ones. We also take into account the quasielastic and inelastic
processes induced by a vector-baryon interaction dominated by vector meson
exchange, as well as the contributions coming from the $\omega \to K \bar K$
mechanism with medium modified $K$, $\bar K$ propagators. We obtain a
substantial increase of the $\omega$ width in the medium, reaching a value of
$129 \pm 10$ MeV at normal nuclear matter density for an $\omega$ at rest,
which comes mainly from $\omega N \to \pi \pi N, \omega N N \to \pi NN$
processes associated to the dominant $\omega \to \rho\pi$ decay mode. The value
of the width increases moderately with momentum, reaching values of around 200
MeV at 600 MeV/c.
