For example, are you asking about:
* The Sambar Deer? They are known to consume leaves, grasses, fruits, and bark.
* The Eld's Deer? Their diet consists mainly of grasses, but they also eat leaves, flowers, and fruits.
* The Hog Deer? These deer are grazers and primarily consume grasses, but will also eat other vegetation like leaves and fruits.
Once you specify the particular Asian Deer you're asking about, I can give you a more precise answer about their diet.