In a medium bowl stir together the lime juice, white wine vinegar, salt, pepper, ginger, basil, thyme, parsley, Tabasco sauce, cayenne pepper and oil. Place the fish fillets into the bowl, cover and marinate for at least 10 minutes or preferably up to 3 hours.
Preheat barbecue for high heat. Discard marinade. Barbecue fish about five minutes each side, until the fish flakes easily with a fork.