@fify-- Yea, tea tree oil is a great ingredient.
I don't use an anti-fungal shampoo but I use it regularly for my horses to keep their skin clean and free from infections. I don't want to advertise the brand, but it's a shampoo made specially for horses and has tea tree oil in it. It also has something called "triclosan." I'm guessing this is another anti-fungal ingredient.
I have a friend who uses this shampoo for her cat and dog too. So I know it's safe for most pets.