An asymptotic analysis of subcritical instability in double diffusive convection is presented. Using a modified perturbation method, a Landau equation that determines how the amplitude of the convection evolves in time is derived. From the Landau equation, it is found that in certain cases, stable finite amplitude convection can exist even when the rest state with no flow is locally stable. The perturbation analysis complements and unifies previous work which is primarily qualitative or numerical in character.