WordWeb Online

1. Offensively self-assured or given to exercising usually unwarranted power
   "a swaggering peremptory manner";
   - autocratic, bossy, dominating, high-and-mighty, magisterial
    
2. Not allowing contradiction or refusal
   "spoke in peremptory tones"; "peremptory commands"
    
3. Putting an end to all debate or action
   "a peremptory decree"

See also: decisive, domineering, imperative

Encyclopedia: Peremptory