Boutros Boutros-Ghali, the incumbent, who is from Egypt, will soon complete his first term, and the United States has made public its desire to see a new person in the job. However, he has indicated he will not go quietly, and a number of countries, including France, have signalled that they would be happy to see him stay in the job.
Mrs Brundtland, 57, Norway's Prime Minister for 10 of the past 15 years, would appear to have excellent qualifications for the post of secretary- general. A strong-minded, hard-working champion of women's rights, environmental issues and Third World development, she led a UN commission that produced a study of the world's environment in 1987 which quickly became known as the Brundtland Report.
It was with her approval that Norwegian officials brokered a peace agreement between Israel and the PLO during a series of secret meetings in Norway. As the NTB news agency observed, "her involvement in international affairs has led to her being known in countries that scarcely would have been aware of Norway otherwise".
However, she is no stranger to controversy. She shocked some of her international admirers in 1992 by announcing Norway would resume whale-hunting in defiance of the International Whaling Commission's world-wide ban.
Mrs Brundtland confined herself yesterday to saying: "I feel I have done a reasonable job for a number of years ... I am in good shape. At 57, one hopes to have many good years to work. I think there are many exciting things I could do."
She told parliament that she had advised Norway's constitutional monarch, King Harald V, to appoint Thorbjoern Jagland, 46, the leader of her own Labour Party, as her successor.
However, she said no one in government or parliament had known about her decision in advance, and she had not even informed Mr Jagland until 10 minutes before her announcement. "We had a little trouble tracking him down. He was out getting a haircut," she said.
Mrs Brundtland became Norway's youngest and first woman prime minister in 1981. Although that spell in office lasted only eight months, she later led two minority Labour governments from 1986 to 1989 and from November 1990 to the present day.
She has been an extraordinarily popular leader, with opinion polls often recording approval ratings of more than 90 per cent. Her popularity was not even affected by what was probably the worst political defeat of her life, the 1994 referendum in which Norwegians voted not to join the European Union.
Being outside the EU seems not to bother a country whose oil and gas wealth has turned it into one of the richest in the world. While most EU countries are grappling with high unemployment, low growth, excessive budget deficits and welfare systems in urgent need of reform, Norway has a booming economy, relatively few people out of work, a budget surplus, and a generous and sophisticated welfare system.
Mrs Brundtland, who studied public health at Harvard University, was elected to parliament in 1977 and took over the Labour Party leadership in 1981. She resigned that job in 1992 after her son Joergen, one of four children, committed suicide.Reuse content