rd This volume contains papers written by the participants of the 3 Workshop on Operator Theory in Krein spaces and Nonlinear Eigenvalue Problems, held at the Technische Universit. at Berlin, Germany, December 12 to 14, 2003. The workshop covered topics from spectral, perturbation and extension t- ory of linear operators in Krein spaces. They included generalized Nevanlinna functions and related classes of functions, boundary value problems for di?erential operators, spectral problems for matrix polynomials, and perturbation problems forsecondorderevolutionequations.Alltheseproblemsarere?ectedinthepresent volume. The workshop was attended by 46 participants from 12 countries. It is a pleasure to acknowledge the substantial ?nancial support received from the - Research Training Network HPRN-CT-2000-00116 Analysis and Operators by the European Community, - DFG-Forschungszentrum MATHEON Mathematik fur .. Schlussel- .. technologien , - Institute of Mathematics of the Technische Universit. at Berlin. We would also like to thank Petra Grimberger for her great help. Last but not least, special thanks are due to Jussi Behrndt, Christian Mehl and Carsten Trunk for their excellent workin the organisationof the workshopand the preparationof this volume. Without their assistance the workshop might not have taken place. The Editors Operator Theory: Advances and Applications, Vol. 162, 1-17 c 2005 Birkh. auser Verlag Basel/Switzerland Partial Non-stationary Perturbation Determinants for a Class of J-symmetric Operators Vadim Adamyan, Peter Jonas and Heinz Langer Abstract. We consider the partial non-stationary perturbation determinant (1) itA ?itH ? (t):=det e P e ,t? R.