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Oscillating flow around a circular cylinder in the vicinity of a plane wall was investigated by solving the two-dimensional incompressible Navier-Stokes equations with a finite element Galarkin residual method. The effect of the gap G/D between the cylinder surface and the wall on the flow behavior was studied. For the case of G/D ≤ 0.25, the periodicity in the flow is attributed to both the outer shear layer instability and the oscillating frequency. As G/D > 0.25, vortex shedding occurs and the periodicity in the flow is mainly due to the competition of the oscillating frequency and the vortex shedding frequency from an isolated stationary cylinder.