During his second term, in December 1972, Kveli joined the Liberal People's Party which split from the Liberal Party over disagreements of Norway's proposed entry to the European Economic Community.
He had previously served in the position of deputy representative during the terms 1961–1965 and 1965–1969.
His political career ended with the post of County Governor of Nord-Trøndelag, which he held from 1979 to 1991.
Kveli is also a former leader of Det Norske Totalavholdsselskap, Norway's oldest temperance organization.
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