1974 To 2008
A tenth place in 1974 was not enough to qualify for the new second division and Cordi became part of the newly recreated Oberliga Nord (III). It remained in this league for the next 17 seasons, without ever coming close to promotion, a fifth place in 1977 being its best result.
In 1991, the club's luck finally run out and it lost its relegation battle, having to step down to the Verbandsliga Hamburg (IV). After an eighth place in its first season there, it earned two championships in the following campaigns, with their second title earning the team promotion to the new Regionalliga Nord (III).
Concordia enjoyed three season there before falling to relegation again and having to return to the Oberliga. After three seasons in the Oberliga Hamburg/Schleswig-Holstein, the club was relegated again, back to the Verbandsliga. A title in this league however moved the team straight back up and it enjoyed three excellent seasons in the Oberliga with two third places in 2003 and 2004 being the best results.
Upon recreation of the Oberliga Nord in 2004, the club was immediately relegated to the Verbandsliga and has since spent its time there. In 2008, the Verbandsliga Hamburg was renamed Oberliga Hamburg. In the final of the Hamburg Cup they won against Altonaer FC 93 with 2:1, so they started in the DFB-Pokal in 2009/2010. There they defeated by TuS Koblenz 0:4.