On representations of matrix valued Nevanlinna functions by u-resolvents

We show that every matrix valued generalized Nevanlinna function can be rep resented asa u-resolvent of a certain selfadjoint relation acting in a Pont ryagin space. The negative index of this Pontryagin space may be larger tha n the number of negative squares of the given function. The minimal index o f negative squares which is needed to obtain such a representation is deter mined. In the case of scalar functions, the results presented give rise to some new classes of generalized Nevanlinna functions.