This paper introduces the Dynamic Evolving Neural-Fuzzy Inference System (DENFIS), a novel type of fuzzy inference system designed for adaptive online and offline learning, particularly for dynamic time series prediction. DENFIS evolves through incremental, hybrid (supervised/unsupervised) learning, accommodating new input data and features by locally tuning elements. New fuzzy rules are created and updated during operation, with the output calculated based on the most activated *m* fuzzy rules from a dynamically chosen fuzzy rule set. Two approaches are proposed: 1) dynamic creation of a first-order Takagi–Sugeno-type fuzzy rule set for online models; 2) creation of a first-order or high-order Takagi–Sugeno-type fuzzy rule set for offline models. The paper also introduces an Evolving Clustering Method (ECM) for both online and offline DENFIS models, which partitions the input space. The effectiveness of DENFIS is demonstrated through its application to the Mackay–Glass (MG) time series, showing superior performance compared to other models like Neural Gas, RAN, EFuNN, and ESOM in online learning, and ANFIS and MLP in offline learning. The paper concludes with directions for further research, including improving online learning and applying DENFIS to adaptive process control and mobile robot navigation.This paper introduces the Dynamic Evolving Neural-Fuzzy Inference System (DENFIS), a novel type of fuzzy inference system designed for adaptive online and offline learning, particularly for dynamic time series prediction. DENFIS evolves through incremental, hybrid (supervised/unsupervised) learning, accommodating new input data and features by locally tuning elements. New fuzzy rules are created and updated during operation, with the output calculated based on the most activated *m* fuzzy rules from a dynamically chosen fuzzy rule set. Two approaches are proposed: 1) dynamic creation of a first-order Takagi–Sugeno-type fuzzy rule set for online models; 2) creation of a first-order or high-order Takagi–Sugeno-type fuzzy rule set for offline models. The paper also introduces an Evolving Clustering Method (ECM) for both online and offline DENFIS models, which partitions the input space. The effectiveness of DENFIS is demonstrated through its application to the Mackay–Glass (MG) time series, showing superior performance compared to other models like Neural Gas, RAN, EFuNN, and ESOM in online learning, and ANFIS and MLP in offline learning. The paper concludes with directions for further research, including improving online learning and applying DENFIS to adaptive process control and mobile robot navigation.