Periodic axial motion of the inner cylinder in Taylor-Couette flow is used to delay transition to Taylor vortices. The outer cylinder is fixed. The marginal stability diagram of Taylor-Couette flow with simultaneous periodic axial motion of the inner cylinder is determined using flow visualization. For the range of parameters studied, the degree of enhanced stability is found to be greater than that predicted by Hu & Kelly (1995), and differences in the scaling with axial Reynolds number are found. The discrepancies are attributed to essential differences between the base flow in the open system considered by Hu & Kelly, where mass is conserved over one period of oscillation, and the base flow in the enclosed experimental apparatus, where mass is conserved at all sections at all times.