  We analyze gravitational waves propagating in an isotropic cosmic fluid
endowed with a bulk viscosity $\zeta$ and a shear viscosity $\eta$, assuming
these coefficients to vary with fluid density $\rho$ as $\rho^\lambda$, with
$\lambda=1/2$ favored by experimental evidence. We give the general governing
equation for the gravitational waves, and focus thereafter on two examples. The
first concerns waves in the very late universe, close to the Big Rip, where the
fate of the comic fluid is dependent highly on the values of the parameters.
Our second example considers the very early universe, the lepton era; the
motivation for this choice being that the microscopical bulk viscosity as
calculated from statistical mechanics is then at maximum. We find that the
gravitational waves on such an underlying medium are damped, having a decay
constant equal to the inverse of the conformal Hubble parameter. Our results
turn out to be in good agreement with other viscosity-based approaches.
