The Rouse model of the dynamics of polymers in solution is generalized by taking into account the hydrodynamic memory during the motion of the polymer monomers in an incompressible liquid. This leads to new peculiarities in the behavior of the time correlation functions describing the polymer motion. It is demonstrated by the appearance of long-time tails of these functions. The mean square displacement of the polymer coil as a whole contains, in addition to the Einstein term similar tot, other contributions, the leading of which is similar tot(1/2). The behavior of the correlation functions for internal modes differs from the traditional exponential relaxation: as t-->infinity, they consist of tails decaying like t(-n/2), the longest-lived being similar tot(-3/2). (C) 2003 American Institute of Physics.