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In this paper, we consider a two-dimensional fluid-rigid body problem. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the dynamics of the rigid body is governed by the conservation laws of linear and angular momentum. The rigid body is supposed to be an infinite cylinder of circular cross-section. Our main result is the existence and uniqueness of global strong solutions. Mathematics Subject Classification (2000). 35Q30, 76D03, 76D05.