Mr Johannesen's predecessor, Joannes Eidesgaard, had stepped down after quarrels with his foreign minister and disagreements within the coalition.
BBC: Faroe Islands
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Mr Johannesen's coalition government consists of nine members representing the Union Party, the People's Party and the Social Democratic Party.
BBC: Faroe Islands
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Kaj Leo Johannesen of the Union Party became prime minister in September 2008, a week after the collapse of former prime minister Joannes Eidesgaard's coalition.