Higher order derivatives of the universal learning network (ULN) has been previously derived by forward and backward propagation computing methods, which can model and control the large scale complicated systems such as industrial plants, economic, social and life phenomena. In this paper, a new concept of nth order asymptotic orbital stability for the ULN is defined by using higher order derivatives of ULN and a sufficient condition of asymptotic orbital stability for ULN is derived. It is also shown that if 3rd order asymptotic orbital stability for a recurrent neural network is proved, higher order asymptotic orbital stability than 3rd order is guaranteed.