A comparative study is presented of two time marching schemes for simulating oscillatory natural convection of low-Prandtl-number fluids in a square cavity. Fully implicit time marching, which is first-order accurate in time, is compared with the second-order-accurate, semi-implicit (Crank-Nicolson) scheme. Both methods are implemented in a control-volume-based finite difference formulation with the central difference scheme used for advection and diffusion terms. Calculations are compared in detail for Gr = 107and Pr = 0.00S, and results for Gr = 106and 3 × 10" are briefly summarized. While both time marching schemes predict oscillatory convection at Gr = 107using an 82 × 82 grid and dimensionless time steps [( Δtα/ L2)Pr√Gr[of 1/80, the flow structure and dynamic behavior predicted by the semi-implicit scheme are more complex than those predicted by the fully implicit scheme. Moreover, it is shown that the semi-implicit calculations are independent of time step while the fully implicit calculations are not.