In a large bowl, stir together the white wine, balsamic vinegar, thyme, oregano, salt and pepper. Place the tuna loin into the marinade, cover and chill in the fridge for 4 hours.
Preheat barbecue for medium heat. Brush the cooking grate with oil, once it is hot.
Place the tuna loin on the cooking grate and discard the marinade. Cook for about 30 minutes, turning frequently for even cooking. Serve immediately when the outer part flakes easily but the centre is still slightly pink.
Can be purchased in speciality fishmongers. You may need to make a special order for it.