Dialogue systems are AI-driven models designed to facilitate natural communication between humans and machines by interpreting input and generating appropriate responses. They are typically categorized as task-oriented systems, which focus on completing specific tasks, and open-domain systems, which engage in general conversations without domain restrictions. Sequence-to-sequence models, originally used in machine translation, have become common in open-domain dialogue systems due to their encoder-decoder structure. RNN-based models, particularly Long Short-Term Memory (LSTM), are frequently utilized for this purpose. However, LSTM faces limitations such as restricted memory capacity and lack of parallel processing. To address these issues, the Extended Long Short-Term Memory (xLSTM) model was developed. In this study, an open-domain dialogue system was created using xLSTM, and its performance was compared with other RNN-based models like Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The DailyDialog dataset was used for training and evaluation, with performance measured by the BLEU score and distinct score to assess the quality of generated responses.