In this paper, a cooperative fuzzy model-predictive control (CFMPC) is presented. The overall nonlinear plant is assumed to consist of several parallel input-coupled Takagi-Sugeno (T-S) fuzzy models. Each such T-S fuzzy subsystem is represented in the form of a local linear model network (LLMN). The control of each local linear model in each LLMN is realized by model-predictive control (MPC). For each LLMN, the outputs of the associated MPCs are blended by the fuzzy membership functions, which leads to a fuzzy model-predictive controller (FMPC). The resulting structure is one FMPC for each LLMN subsystem. Overall, a parallel combination of FMPCs results, which mutually affects all LLMN subsystems by their respective manipulated variables. To compensate detrimental cross-couplings in this setup, a cooperation between the FMPCs is introduced. For this cooperation, convergence is proven, and for the closed-loop system, a stability proof is given. It is demonstrated in a simulation example that the proposed input-constraint CFMPC algorithm achieves convergence of the fuzzy LLMNs within few cooperative iteration steps. Simulations are given to demonstrate the effectiveness of the theoretical results.