Beckmeyer has been a member of the SPD since 1969 and was chairman of the SPD district of Bremerhaven from 1972 to 1987. On 25 March 2006, he was elected as regional chairman of the SPD in the state of Bremen.
From 1975 to 1987, as well as from 1999 to 2002, Beckmeyer was a member of the parliament of Bremen. There, he was deputy chairman of the SPD faction from 1979 to 1987.
From 2002 until 2017, Beckmeyer was a member of the German federal parliament, where he holds the office of speaker of the task group for traffic, construction and town development of the SPD's faction since 2004. In December 2005, he also became a member of the parliamentary group's executive committee.
Beckmeyer always entered the federal parliament as a directly elected candidate for the Bremen II – Bremerhaven constituency. At the 2005 German federal election he won 54.4% of first votes.[1]
On 15 October 1987, Beckmeyer was appointed as a senator for economics, technology and foreign trade into the senate of the free Hanseatic city Bremen, led by president of the senate Klaus Wedemeier. After the 1991 parliamentary elections in Bremen, he became senator for ports, navigation and foreign trade on 11 December 1991, and also senator for federal matters.
With the assumption of office of Henning Scherf as new mayor and president of the senate Beckmeyer on 4 July 1995, Beckmeyer was elected as senator for ports, supraregional traffic and foreign trade as well as senator for employment. After the elections to the Bremen parliament of 1999, he abandoned his public positions on 7 July 1999.