A numerical study is presented of unsteady double-diffusive convection in a square cavity with equal but opposing horizontal temperature and concentration gradients. The boundary conditions along the vertical side-walls are imposed in such a way that the buoyancy ratio N = Gr(S)/Gr(T) is equal to -1, where Gr(S) and Gr(T) are the solutal and thermal Grashof numbers, respectively. In this situation, steady-state convective flow is stable up to a threshold value Gr(cl) of the thermal Grashof number which depends on the Lewis number Le. Beyond Gr(cl), oscillatory convective flows occur. Here we study the transition, steady-state flow-oscillatory flow, as a function of the Lewis number. The Lewis number varies between 2 and 45. Depending on the values of the Lewis number, the oscillatory flow occurring for Gr(T) slightly larger than Gr(cl) is either centro-symmetric (for Le greater than or equal to 17) or asymmetric single frequency flow (for Le less than or equal to 17). For larger values of the thermal Grashof number, the two regimes occur for fixed values of Gr(T) and Le. Furthermore, computations show that Gr(cl) reaches a minimum equal to 4.75 x 10(4) for Le approximate to 7.