Combine marinade ingredients in small bowl. Remove and reserve 2 tablespoons. Place beef steaks and remaining marinade in food-safe plastic bag; turn steaks to coat. Close bag securely and marinate in refrigerator 15 minutes to 2 hours.
Place asparagus in shallow microwave-safe dish; add 1/2 cup water. Cover and microwave on HIGH 3 to 6 minutes or until crisp-tender. Drain asparagus. Add reserved 2 tablespoons marinade to asparagus; turn to coat. Set aside.
Remove steaks from marinade; discard marinade. Place steaks on grid over medium, ash-covered coals. Grill, covered, 7 to 11 minutes (over medium heat on preheated gas grill, 8 to 13 minutes) for medium rare (145°F) doneness, turning once. (Do not overcook.)
During last 3 minutes of grilling, arrange asparagus on grid around steaks; grill 2 to 3 minutes, turning once. Season steaks and asparagus with salt and pepper.
Nutrition information per serving: 366 Calories; 126 kcal Calories from fat; 14 g Total Fat; 4 g Saturated Fat; 4 g Monounsaturated Fat; 149 mg Cholesterol; 591 mg Sodium; 7 g Total Carbohydrate; 2.5 g Dietary Fiber; 52 g Protein; 4.4 mg Iron; 8.4 mg Niacin; 0.6 mg Vitamin B6; 2.6 mcg Vitamin B12; 8 mg Zinc; 52.9 mcg Selenium;