There are at least two bands with this name:

1)Big Time was Serbian blues-rock band from Trstenik.

Band members:
Pantović Nikola - Panta - vocals, lead & rhythm guitar
Ivan Veljović - Velja - lead guitar
Dejan Todosijević - Deja - acoustic guitar
Ivan Radovanović - Ica - bass guitar
Dragan Pelivanović - Gagac - drums

Discography:
Cracked (2000)
Rađanje novog sunca (2002)

2)Big Time is a Swedish eurodance project.
The members were the rapper AJ Soliter and the female vocalist Beatrice Ray.
The group was established in 1994 by the German-eurodance producer Stefan Rugheri. Their first single to be released was Summertime Is Crazy. It reached top 40 in Belgium, Germany, Austria and Canada. It was also No.1 in Russia and Brasil. Read more on Last.fm. User-contributed text is available under the Creative Commons By-SA License; additional terms may apply.