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Training LLMs with Mixture-of-Experts (MoE) architecture on long sequences poses significant challenges due to the all-to-all communication bottleneck of expert parallelism. While existing approaches attempt to hide the communication costs in computation through token-level pipelining within MoE layers, their effectiveness is limited by the insufficient computation. We present FoldMoE, a high-performance MoE training system that enables token-level overlapping across entire Transformer blocks through novel attention-MoE pipelining. We propose an efficient pipeline schedule, and a novel token buffering design to decouple attention and MoE layer partitioning, along with a time-uniform micro-batching strategy for enhanced efficiency. Evaluations on GPT-MoE models with sequences up to 32K tokens show that FoldMoE achieves up to 1.49x and 2.72x speedup over state-of-the-art token-level overlapping and non-overlapping baselines respectively.