  The $\omega$ and $\phi$ mesons are exceptionally narrow in vacua being about
8 and 4 MeV. At finite temperature they will scatter with other hadrons in
their approach to equilibrium and thereafter. These dynamics induce broadening
to the already unstable vector mesons which is calculated in the framework of
relativistic kinetic theory. A rather complete set of low-lying mesons provide
reaction partners whose interactions are modeled using effective Lagrangians.
Collision rates for $\rho$ and $\omega$ are found to be $\sim$ 100 MeV at
$T$=200 MeV while the rate for $\phi$ is $\sim$ 25 MeV. Corresponding mean free
paths are about 1 and 4 fm! Possible observable consequences are discussed.
