This paper gives an analytical method to determine the existence of the long period mode which is the most typical rhythmic activity in reciprocal inhibition networks. The network is assumed to have a considerable odd number of neurons in a ring structure of a linear array. In the long period mode, each cell has the active and the quiescent phases. A number of firings are seen at the constant interval in the active phase, while the firings are inhibited in the quiescent phase. It is shown that there exist many firing patterns in this mode, and that the period length of the rhythmic activities is different depending on the number of firings in the active phases. The upper bound of the period length increases with the increase of the number of cells. Since various firing patterns are possible to occur under identical input and structure parameters, occurrence of each firing pattern of the long period mode has to be determined by a suitable selection of initial conditions of the network. Relations between the firing patterns and the initial conditions are studied in terms of phase transition delay time.