The nonlinear aspects of the instability of the wake behind an aligned flat plate are studied in the long-wavelength regime using asymptotic solutions of the unsteady Euler equations. Equations are obtained to describe the nonlinear evolution of the vortex-layer interface formed just downstream of the trailing edge. It is found that the instability is driven by a pressure jump across this layer, which has the same form as that arising from surface-tension effects, but with a negative (destabilizing) sign. The simplified case of a bounded wake is formulated and computed numerically. Comparisons with experiments show qualitative agreement.