She has been a member of the Luxembourg Socialist Workers' Party since 1974 and in 1987 became a member of the city council of Luxembourg.
She gave up her teaching post in 1989 when she entered government as secretary of State for Health, Social Security, Youth, and Sport.
She was Minister for Transport between 1994 and 1999, and from 2004 to 2013 Minister for Education.
Since 2014 she is member of the European Parliament.
In 2017, A robot tax had previously been part of Delvaux's bill imposing ethical standards for robots in the European Union.
However, the European Parliament rejected this aspect when it voted on the law.