GNU Collaborative International Dictionary of English

Found one definition

1.       
   gaga adj.
   1.  mentally or physically infirm with age.
   
   Syn. -- doddering, senile.
   
   [WordNet 1.5]
   
   
   2.  marked by foolish or unreasoning fondness; as, “gaga over his girlfriend”.
   
   Syn. -- crazy about, dotty, enamored, infatuated, in love, smitten, soft on(predicate), taken with(predicate).
   
   [WordNet 1.5]