Continual Test-Time Adaptation (CTTA) generalizes conventional Test-Time Adaptation (TTA) by assuming that the target domain is dynamic over time rather than stationary. In this paper, we explore Multi-Modal Continual Test-Time Adaptation (MM-CTTA) as a new extension of CTTA for 3D semantic segmentation. The key to MM-CTTA is to adaptively attend to the reliable modality while avoiding catastrophic forgetting during continual domain shifts, which is out of the capability of previous TTA or CTTA methods. To fulfill this gap, we propose an MM-CTTA method called Continual Cross-Modal Adaptive Clustering (CoMAC) that addresses this task from two perspectives. On one hand, we propose an adaptive dual-stage mechanism to generate reliable cross-modal predictions by attending to the reliable modality based on the class-wise feature-centroid distance in the latent space. On the other hand, to perform test-time adaptation without catastrophic forgetting, we design class-wise momentum queues that capture confident target features for adaptation while stochastically restoring pseudo-source features to revisit source knowledge. We further introduce two new benchmarks to facilitate the exploration of MM-CTTA in the future. Our experimental results show that our method achieves state-of-the-art performance on both benchmarks.