In this paper two different fuzzy-neural systems with reduced fuzzy rules bases, namely Distributed Adaptive Neuro Fuzzy Architecture (DANFA) and Semi Fuzzy Neural Network (SFNN), are presented. Both structures are realized with Takagi-Sugeno fuzzy inference mechanism and they posses reduced number of parameters for update during the learning procedure. Thus, the computational time for algorithm execution is additionally reduced, which make the modeling structures a promising solution for real time applications. As a learning approach for the designed structures a simplified two-step gradient descent approach is implemented. To demonstrate the potentials of both models, simulation experiments with two benchmark chaotic time systems—Mackey-Glass and Rossler are studied. The obtained results show accurate models performance with minimal prediction error.