  In this paper, we have obtained motion equations for a wide class of
one-dimensional singularities in 2-D ideal hydrodynamics. The simplest of them,
are well known as point vortices. More complicated singularities correspond to
vorticity point dipoles. It has been proved that point multipoles of a higher
order (quadrupoles and more) are not the exact solutions of two-dimensional
ideal hydrodynamics. The motion equations for a system of interacting point
vortices and point dipoles have been obtained. It is shown that these equations
are Hamiltonian ones and have three motion integrals in involution. It means
the complete integrability of two-particle system, which has a point vortex and
a point dipole.
