  In this paper the small-amplitude motion of multiple superposed viscous
fluids is studied as a linearized initial-value problem. The analysis results
in a closed set of equations for the Laplace transformed amplitudes of the
interfaces that can be inverted numerically. The derived equations also contain
the general normal mode equations, which can be used to determine the
asymptotic growth-rates of the systems directly. After derivation, the
equations are used to study two different problems involving three fluid layer.
The first problem is the effect of initial phase difference on the development
of a Rayleigh-Taylor instability and the second is the damping effect of a
thin, highly viscous, surface layer.
