We give the recurrence relations, interpolating properties and convergence
results for a sequence of orthogonal rational functions of increasing
order that have fixed poles in some region O of the complex plane.
They are orthogonalized with respect to a measure supported on the boundary S of O.
We give formulations of the results which are valid for S equal to the
unit circle or the real line. The corresponding region O is then the
exterior of the unit disk or the lower half plane.