  Given that observations seem to favour a \index{density parameter}
$\Omega_0<1$, corresponding to an open universe, we consider gauge\hs invariant
perturbations of non\hs flat Robertson\hs Walker universes filled with a
general imperfect fluid which can also be taken to represent a scalar field.
Our aim is to set up the equations that govern the evolution of the density
perturbations $\Delta$ so that it can be determined through a {\it first order
differential equation} with a quantity $\kk$ which is conserved at any length
scale, even in non\hs flat universe models, acting as a source term. The
quantity $\kk$ generalizes other variables that are conserved in specific cases
(for example at large scales in a flat universe) and is useful to connect
different epochs in the evolution of density perturbations via a transfer
function. We show that the problem of finding a conserved $\kk$ can be reduced
to determining two auxiliary variables $X$ and $Y$, and illustrate the method
with two simple examples.
