In this chapter, the error convergence of the sequential adaptive fuzzy inference system (SAFIS) and the modified sequential adaptive fuzzy inference system (MSAFIS) is analyzed. SAFIS utilizes the extended Kalman filter, while MSAFIS uses the gradient descent technique. First, proposed algorithms are linearized to get their modeling dynamic equations. Second, Lyapunov strategy is utilized to ensure the error convergence of studied networks. Two examples show the performance of advised algorithms.