Previous video object segmentation approaches mainly focus on using simplex solutions between appearance and motion, limiting feature collaboration efficiency among and across these two cues. In this work, we study a novel and efficient full-duplex strategy network (FSNet) to address this issue, by considering a better mutual restraint scheme between motion and appearance in exploiting the cross-modal features from the fusion and decoding stage. Specifically, we introduce the relational cross-attention module (RCAM) to achieve bidirectional message propagation across embedding sub-spaces. To improve the model's robustness and update the inconsistent features from the spatial-temporal embeddings, we adopt the bidirectional purification module (BPM) after the RCAM. Extensive experiments on five popular benchmarks show that our FSNet is robust to various challenging scenarios (e.g., motion blur, occlusion) and achieves favourable performance against existing cutting-edges both in the video object segmentation and video salient object detection tasks. The project is publicly available at: https://dpfan.net/FSNet.