One specimen nicknamed "Oymiakon" - believed to be a 1-year-old female that lived between 28,000 B.C. and 38,000 B.C. - was being shown outside Russia for the first time since its discovery in the Siberian permafrost in 2004, organizers said.
Only her tusk-less head was uncovered, and the rest of the remains may have decomposed or were eaten by other animals, said zoologist Lin Chun-tsong.
The second mammoth, called "Yukagir," a 40-year-old male that lived around 18,000 B.C., is complete with two long curving tusks, hairy head and part of a leg. It was first seen by the public at Japan's Aichi Expo in 2005, after being excavated in 2002.
Some experts believe the mammoths were discovered because of Siberia's melting permafrost, said Hsiang Kuo-ning, director of the United Evening News, which co-sponsors the exhibition.
The mammoth remains were provided by Russia's Sakha Republic, where they were discovered. The exhibition will run through Nov. 4.