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A perturbation analysis based on equations of motion in Lagrangian form is presented for the oscillatory and time-mean viscous flows induced by a propagating wave of small amplitude in an annulus with a viscoelastic outer wall.Owing to the steady streaming effect,the existence of a catheter in a blood vessel brings in an additional steady pressure gradient,a correction to that predicted by the linear theory,and an additional steady shear stress,which may increase the possibility of hemolysis of red blood cells.