The globally connected active rotators with excitatory and inhibitory connections having different time constants under noise are analyzed using the nonlinear Fokker-Planck equation, and their oscillatory phenomena are investigated. Based on numerically calculated bifurcation diagrams, both periodic solutions and chaotic solutions are found. The periodic firings are classified based on the firing period, the coefficient of variation, and the correlation coefficient, and weakly synchronized periodic firings which are often observed in physiological experiments are found.