  In this paper the realization problems for the Krein-Langer class $N_\kappa$
of matrix-valued functions are being considered. We found the criterion when a
given matrix-valued function from the class $N_\kappa$ can be realized as
linear-fractional transformation of the transfer function of canonical
conservative system of the M. Livsic type (Brodskii-Livsic rigged operator
colligation) with the main operator acting on a rigged Pontryagin space $\Pk$
with indefinite metric. We specify three subclasses of the class $N_\kappa(R)$
of all realizable matrix-valued functions that correspond to different
properties of a realizing system, in particular, when the domains of the main
operator of a system and its conjugate coincide, when the domain of the
hermitian part of a main operator is dense in $\Pi\kappa$. Alternatively we
show that the class $N_\kappa(R)$ can be realized as transfer matrix-functions
of some canonical impedance systems with self-adjoint main operators in rigged
spaces $\Pk$. The case of scalar functions of the class $N_\kappa(R)$ is
considered in details and some examples are presented.
