This paper describes some dynamical properties of higher order neural networks with decreasing energy functions. First, we will show that for any symmetric higher order neural network which permits only one element to transit at each step, there are only periodic sequences with the length 1. Further, it will be shown that for any higher order neural network, with decreasing energy functions, which permits all elements to transit at each step, there does not exist any periodic sequence with the length being over k + 1, where k is the order of the network. Lastly, we will give a characterization for higher order neural networks, with the order 2 and a decreasing energy function each, which permit plural elements to transit at each step and have periodic sequences only with the lengh 1.