In this work, we propose a new efficient solution, which is a Mamba-based model named BMACE (Bidirectional Mamba-based network, for Automatic Chord Estimation), which utilizes selective structured state-space models in a bidirectional Mamba layer to effectively model temporal dependencies. Our model achieves high prediction performance comparable to state-of-the-art models, with the advantage of requiring fewer parameters and lower computational resources, while still captureing and leveraging long-term dependencies.