The paper introduces the Dynamic Evolving Neural-Fuzzy Inference System (DENFIS), a novel fuzzy inference system designed for adaptive online and offline learning and time series prediction. DENFIS evolves through incremental, hybrid (supervised/unsupervised) learning, accommodating new input data and creating new fuzzy rules dynamically. It uses a Takagi-Sugeno-type fuzzy rule set, either first-order or expanded high-order, for online and offline models. DENFIS can insert or extract fuzzy rules during learning and employs an evolving clustering method (ECM) for partitioning the input space. The system is demonstrated to effectively learn complex temporal sequences and outperform existing models in time series prediction tasks. The paper compares DENFIS with other models like ANFIS, MLP-BP, RAN, EFuNN, and ESOM, showing its superiority in both online and offline learning scenarios. DENFIS is applied to predict the Mackey-Glass and Gas-furnace time series, achieving better performance in terms of prediction accuracy and efficiency. The study highlights the potential of DENFIS for adaptive learning and real-time applications in intelligent systems.The paper introduces the Dynamic Evolving Neural-Fuzzy Inference System (DENFIS), a novel fuzzy inference system designed for adaptive online and offline learning and time series prediction. DENFIS evolves through incremental, hybrid (supervised/unsupervised) learning, accommodating new input data and creating new fuzzy rules dynamically. It uses a Takagi-Sugeno-type fuzzy rule set, either first-order or expanded high-order, for online and offline models. DENFIS can insert or extract fuzzy rules during learning and employs an evolving clustering method (ECM) for partitioning the input space. The system is demonstrated to effectively learn complex temporal sequences and outperform existing models in time series prediction tasks. The paper compares DENFIS with other models like ANFIS, MLP-BP, RAN, EFuNN, and ESOM, showing its superiority in both online and offline learning scenarios. DENFIS is applied to predict the Mackey-Glass and Gas-furnace time series, achieving better performance in terms of prediction accuracy and efficiency. The study highlights the potential of DENFIS for adaptive learning and real-time applications in intelligent systems.