Combine steak sauce, brown sugar and lime juice, reserving 2 tablespoons of this marinade.
Place beef in plastic bag and add remaining marinade, turning to coat.
Close bag securely and marinate for 10 minutes.
Pour off marinade and grill steaks for 14 to 20 minutes for rare to medium done.
Brush with reserved 2 tablespoons of marinade during last 2 minutes of cooking.