WordWeb Online

1. Under normal conditions
   "normally she was late";
   - usually, unremarkably, commonly, ordinarily
    
2. Most of the time; in most cases
   "normally it doesn't rain much here";
   - by and large, generally, more often than not, mostly, in general, on the whole, typically, ordinarily, as a rule, usually
    
3. In a natural or normal manner
   "speak normally and easily";
   - naturally

Antonym: notably

Encyclopedia: Normally