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This paper introduces a class of evolving fuzzy rule-based system as an approach for multivariable Gaussian adaptive fuzzy modeling. The system is an evolving Takagi-Sugeno (eTS) functional fuzzy model, whose rule base can be continuously updated using a new recursive clustering algorithm based on participatory learning. The fuzzy sets of the rule antecedents are multivariable Gaussian membership functions, which have been adopted to preserve information between input variable interactions. The parameters of the membership functions are estimated by the clustering algorithm. A weighted recursive least-squares algorithm updates the parameters of the rule consequents. Experiments considering time-series forecasting and nonlinear system identification are performed to evaluate the performance of the approach proposed. The multivariable Gaussian evolving fuzzy models are compared with alternative evolving fuzzy models and classic models with fixed structures. The results suggest that multivariable Gaussian evolving fuzzy modeling is a promising approach for adaptive system modeling.