A solution of hydrodynamic equations for the case of (Taylor) instability of the interface of two fluids of different but constant densities when accelerated from the heavier fluid to the lighter fluid is sought. After identifying the problem as one of singular perturbation, it is solved by the method of strained coordinates. A third order theory is presented. It is found that the ratio of the densities of the fluids has a significant effect on the stability or growth of the interface. Growth of the interface is found to depend also on the wave number and amplitude of initial disturbance. Stability criterion is calculated for different values of density ratio. © 1976 Springer-Verlag.