As a single skater König came 3rd at the junior world championships 1982. His greatest success, however, was in pair skating where he and Scwartz won the bronze medal in the 1988 European Cup.
In 1990 Peggy Schwarz and Alexander König changed their coach to Knut Schubert. The couple split in 1994 as Schwarz was pregnant. At this time Alexander König also finished his figure skating career.
From 1985 to 1988 Alexander König attended school to became a specialist in gastronomy. From 1994 to 1997 he studied sport at the Trainerakademie in Cologne. He is an A-licenced coach of the DEU (German figure skating union). Already during his education he worked as a coach in Stuttgart, and following his graduation he took a job as a coach in Chemnitz. From 2001 to 2008 Alexander König worked as a figure skating coach in Berlin. He is also figure skating judge and technical specialist. He moved to Oberstdorf in the summer of 2008 to coach there.
Since 1983 he has also a successful painter and has had several exhibitions for his paintings.