The equations describing the first two ternas of an asymptotic expansión of the solution of the planar turbulent mixing layer for valúes of the velocity ratio cióse to one are obtained. The first term of this expansión is the solution of the well-known time-evolving probiem and the second, which includes the efFects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.