Normal del Pezzo surfaces containing a nonrational singularity

Working over perfect ground fields of arbitrary characteristic, I classify minimal normal del Pezzo surfaces containing a nonrational singularity. As an application, I determine the structure of 2-dimensional anticanonical models for proper normal algebraic surfaces. The anticanonical ring may be non-finitely generated. However, the anticanonical model is either a proper surface, or a proper surface minus a point. Received: 5 June 2000 / Revised version: 10 November 2000