She was elected to the Norwegian Parliament from Hordaland in 1993, and was re-elected on one occasion. She served as a deputy representative during the terms 1989–1993 and 2001–2005. Three years into the second term as deputy, she replaced the regular representative Leif Lund who died.
Tveiten was a member of Osterøy municipality council from 1983 to 1987. During this term she was also a member of Hordaland county council.
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