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 = GrS⧹GrT is equal to −1, where GrS and GrT are the solutal and thermal Grashof numbers, respectively. In this situation, steady-state convective flow is stable up to a threshold value Grc1 of the thermal Grashof number which depends on the Lewis number Le. Beyond Grc1, 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 GrT slightly larger than Grc1 is either centro-symmetric ( for Le ⩾ 17) or asymmetric single frequency flow ( for Le ⩽ 17) . For larger values of the thermal Grashof number, the two regimes occur for fixed values of GrT and Le. Furthermore, computations show that Grc1 reaches a minimum equal to 4.75×104 for Le ≈ 7