  We consider the motion of rigid bodies in a potential fluid subject to
certain nonholonomic constraints and show that it is described by
Euler--Poincar\'e--Suslov equations.
  In the 2-dimensional case, when the constraint is realized by a blade
attached to the body, the system provides a hydrodynamic generalization of the
Chaplygin sleigh, whose dynamics are studied in detail. Namely, the equations
of motion are integrated explicitly and the asymptotic behavior of the system
is determined. It is shown how the presence of the fluid brings new features to
such a behavior.
