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The flow between eccentric rotating cylinders when either the outer or inner cylinder is stationary is analysed both for the creeping flow approximation and for the case when inertial effects are not negligible. Numerical solutions are obtained using a finite difference ADI scheme and a fine orthogonal bipolar coordinate grid. When the centres of the two cylinders are far enough, a two‐dimensional recirculation zone appears in the region where the gap spacing is greatest. On increasing the eccentricity, the recirculation zone becomes bigger and the separation and reattachment points move towards the region of narrowest gap. Further increase of the eccentricity results in the formation of a saddle point between the cylinders at the region of narrowest gap. As the Reynolds numbers increases, inertial effects modify slightly the recirculation region; the separation point moves upstream and the reattachment point moves downstream when either the inner or the outer cylinder rotate.