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I Don't Want to Miss a Thing" is a hit single by American rock band Aerosmith. It was taken from the Armageddon soundtrack and debuted at number one on the Billboard Hot 100, becoming the first and only song by a rock band to debut at #1 [1]. The song stayed at number one for four weeks from September 5 to September 26, 1998. It also introduced Aerosmith to a whole new generation of fans. The song rose steadily up the charts in the UK, peaking at number four in November 1998. It remains one of Aerosmith's most popular songs and is widely credited as the song that introduced Aerosmith to a new generation (Generation Y).
This song is definitely originally by Aerosmith. Perhaps other artists such as bon jovi re-sing it due to its popularity.