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 griller for high heat without the tray.
Lightly oil griller tray. Add the tuna steaks, cook for 5 to 6 minutes, then turn and baste with the marinade. Cook for an additional 5 minutes, or till done to your liking. Discard any remaining marinade.