WordNet (r) 3.0 (2006):

big league
    n 1: the most important league in any sport (especially
         baseball) [syn: major league, big league, majors]

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "big league":
   big, big-name, big-time, bigwig, bigwigged, consequential,
   considerable, double-barreled, earthshaking, grand, great,
   heavyweight, high-powered, important, major, material, momentous,
   name, self-important, significant, substantial, superior,
   world-shaking