Max Kock, familiarly known to all as Max, is a retired policeman who saved Moser from a life of crime and became something of a mentor to him. Many early episodes feature Moser asking Koch for advice - often in a café or a pool hall. It is, in fact, advice from Koch which is responsible for solving many of the more baffling cases, as his insights into human psychology - particularly female psychology (something he often claims Moser has had no knowledge of since his divorce) - prove correct.
Max is also occasionally asked to look after Rex, and Rex seems to be comfortable with him.
As the series progresses, Koch's role alters to that of being a useful spy for Moser in certain situations where his team is too well-known. It is Koch's visit to a restaurant which provides the breakthrough in one case. In another he stumbles upon the solution to a particularly brutal homicide while sitting in a park with Rex. Koch is increasingly reluctant to help Moser with his work, although he is always told that this will be the last time. As Stockinger points out, it always is the last time… until the next request. Moser also tries to appeal to Koch's sense of adventure which, as Max famously explains, is satisfied by eating goulash and not knowing if he will suffer from "Rinderwahnsinn" (Mad Cow Disease).
Following Stockinger's transfer to Salzburg, Koch assists the team to reorganise the office. His snide remarks about Stockinger's files result in Höllerer telling him to read through them all (to which Koch responds that he's doing more work since he retired than he did when he worked). He also spreads out his pipe collection on Stocki's old desk and declares that he will "open a pipe shop" while the team attempts to find a replacement for Stocki.
He leaves the series after Moser dies.