  Dynamical stability of the shock compressed layer with finite thickness is
investigated. It is characterized by self-gravity, structure, and shock
condition at the surfaces of the compressed layer. At one side of the shocked
layer, its surface condition is determined via the ram pressure, while at the
other side the thermal pressure supports its structure. When the ram pressure
dominates the thermal pressure, we expect deceleration of the shocked layer.
Especially, in this paper, we examine how the stratification of the
decelerating layer has an effect on its dynamical stability. Performing the
linear perturbation analysis, a {\it more general} dispersion relation than the
previous one obtained by one of the authors is derived. It gives us an
interesting information about the stability of the decelerating layer.
Importantly, the DSI (Decelerating Shock Instability) and the gravitational
instability are always incompatible. We also consider the evolution effect of
the shocked layer. In the early stages of its evolution, only DSI occurs. On
the contrary, in the late stages, it is possible for the shocked layer to be
unstable for the DSI (in smaller scale) and the gravitational instability (in
larger scale). Furthermore, we find there is a stable range of wavenumbers
against both the DSI and the gravitational instability between respective
unstable wavenumber ranges. These stable modes suggest the ineffectiveness of
DSI for the fragmentation of the decelerating slab.
