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Sweden's King Carl Gustaf presented the awards amid trumpet fanfares and speeches by members of the Nobel committees in medicine, physics, chemistry, economics and literature at Stockholm's Concert Hall.
Albert Fert, of France, and Peter Gruenberg, of Germany, received the physics prize.
The chemistry prize was awarded to Germany's Gerhard Ertl for his studies of chemical reactions on solid surfaces.
The oldest laureates, literature prize winner Doris Lessing, 88, and economics co-winner Leonid Hurwicz, 90, were not able to travel to Stockholm for health reasons.
Meanwhile, the Nobel Peace Prize was awarded in Oslo, Norway, to climate campaigner Al Gore and the UN's Intergovernmental Panel on Climate Change, or IPCC.
Dr. Rajendra K. Pachauri is the head of IPCC.
"Will those responsible for decisions in the field of climate change at the global level listen to the voice of science and knowledge, which is loud and clear? If they do so at Bali and beyond then all my colleagues in the IPCC and those thousands toiling for the cause of science would feel doubly honoured at the privilege I am receiving today on their behalf."
The 1.6 million US dollar awards were announced in October but are always presented in the two Scandinavian capitals on December 10 to mark the anniversary of the 1896 death of their creator, Alfred Nobel.
The first Nobel Prizes were handed out in 1901.