  In this paper we consider two related objects: singular positive semidefinite
Hankel block--matrices and associated degenerate truncated matrix Hamburger
moment problems. The description of all solutions of a degenerate matrix
Hamburger moment problem is given in terms of a linear fractional
transformation. The case of interest is the Hamburger moment problem whose
Hankel block--matrix admits a positive semidefinite Hankel extension.
