The effect of compressibility and of density variation on Rayleigh–Taylor and Richtmyer–Meshkov instability of the temporal development of two fluid interfacial structures such as bubbles and spikes have been investigated. It is seen that the velocity of the tip of the bubble or spike increases (destabilization) if the local Atwood number increases due to density variation of either of the fluids. The opposite is the result, i.e., the bubble or spike tip velocity decreases (stabilization) if the density variation leads to lowering of the value of the local Atwood number. The magnitude of stabilization or destabilization is an increasing function of the product of the wave number k and interfacial pressure p₀. The effect of compressibility is quite varied. If the heavier (upper) fluid alone is incompressible (g_h→ ¥), but the lighter fluid is compressible the growth rate is higher
(destabilization) than when both the fluids are incompressible. Moreover the heavier fluid remaining incompressible the growth rate decreases (stabilization) as (finite) increases and ultimately tends to the incompressible limit value as g_l→ ¥. With  g_l→ ¥ but g_h finite the growth increases (destabilization) as g_h increases. When both g_h and g_l are finite (density r_h>density r_l) the growth is reduced when g_h > g_l compared to that when both fluids are incompressible and enhanced when
g_h > g_l. The set of nonlinear equations describing the dynamics of bubbles and spikes in the presence of fluid density variations are not analytically integrable in closed form. The results derived by numerical solution methods are represented and interpreted in corresponding figures.