With the rapid advancement of science and technology, nonlinear distortion in signals has become an increasingly pressing issue, attracting growing attention from both academia and industry. This issue has raised concerns over the costs and thermal challenges involved in the linearization of output signals. This paper presents a digital predistortion (DPD) method based on a dual-stage learning architecture that utilizes the extended long short-term memory (xLSTM) network. The proposed method uses xLSTM to separately model the nonlinearity of power amplifiers (PA) and DPD, addressing the limitations of traditional LSTM networks, such as the inability to modify stored decisions, limited storage capacity, and performance degradation caused by additional operations in conventional learning architectures. Experimental results on real datasets validate the effectiveness of the proposed method, showing significant improvements in the linearization of distorted signals compared to existing approaches.