  Let, J, be an m-by-m-signature matrix and let D be the open unit disk in the
complex plane. Denote by P{J,0}(D) the class of all meromorphic
m-by-m-matrix-valued functions, f, in D which are holomorphic at 0 and take
J-contractive values at all points of D at which f is holomorphic. The central
theme of this paper is the study of the following interpolation problem:
  Let n be a nonnegative integer, and let A_0, A_1, ..., A_n be a sequence of
complex m-by-m-matrices. Describe the set of all matrix-valued functions, f,
belonging to the class P{J,0}(D), such that the first n+1 Taylor coefficients
of f coincide with A_0, A_1, ..., A_n. In particular, we characterize the case
that this set is non-empty.
  In this paper, we will solve this problem in the most general case. Moreover,
in the non-degenerate case we will give a description of the corresponding Weyl
matrix balls. Furthermore, we will investigate the limit behaviour of the Weyl
matrix balls associated with the functions belonging to some particular
subclass of P{J,0}(D).
