Accurate traffic flow prediction plays a vital role in intelligent transportation systems, yet existing deep learning approaches still face challenges in modeling complex long-range spatio-temporal dependencies and handling the inherent non-stationarity of traffic data. To address these issues, we propose CTMamba, a hybrid Transformer–Mamba architecture that integrates cross-temporal fusion, memory-based spatial attention, and selective state space modeling for efficient and adaptive traffic flow prediction. Specifically, the Cross-Temporal Fusion Embedding Module (CTFEM) introduces a temporal smoothing mechanism by combining the moving average of recent time windows with the latest observation, providing a stable reference that mitigates temporal non-stationarity. The Spatial Memory Attention (SMA) module employs a learnable memory matrix to efficiently capture dynamic spatial dependencies among nodes with linear computational complexity. Furthermore, the TMamba module leverages selective state space modeling combined with temporal convolution to capture long-range temporal dependencies while maintaining scalability. Extensive experiments on four real-world traffic datasets demonstrate that CTMamba consistently outperforms state-of-the-art baselines in both prediction accuracy and efficiency. Ablation analyses further confirm that the proposed CTMamba design effectively alleviate data non-stationarity and enhance spatio-temporal representation learning.