The relative motion of two vortex filaments (two dimensional point vortices) with arbitrary strengths in presence of an infinite rigid wall is qualitatively analized. Hamiltonian for the system is obtained by use of met hod of images and the integrability is proved.
The feature of relative motion are classified according to k, the ratio of strengths of two vortices, and the value of system Hamiltonian. For typical cases, trajectories of two vortices are calculated numerically.