In a large non-reactive dish, mix together the orange juice, soy sauce, olive oil, lemon juice, parsley, garlic, oregano, and pepper. Place the tuna steaks in the marinade and turn to coat. Cover, and refrigerate for at least 30 minutes.
Preheat grill for high heat.
Lightly oil grill grate. Cook the tuna steaks for 5 to 6 minutes, then turn and baste with the marinade. Cook for an additional 5 minutes, or to desired doneness. Discard any remaining marinade.