  Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood
of some compact subset E of the complex plane, we give necessary and sufficient
conditions for the convergence with geometric rate of the common denominators
of multipoint Hermite-Pade approximants. The exact rate of convergence of these
denominators and of the approximants themselves is given in terms of the
analytic properties of the system of functions. These results allow to detect
the location of the poles of the system of functions which are in some sense
closest to E.
