The expansion of large language models is increasingly limited by the constrained memory capacity of modern GPUs. To mitigate this, Mixture-of-Experts (MoE) architectures activate only a small portion of parameters during inference, significantly lowering both memory demand and computational overhead. However, conventional MoE inference approaches, which select active experts independently at each layer, often introduce considerable latency because of frequent parameter transfers between host and GPU memory. In addition, current cross-layer prediction strategies, which are typically based on fixed steps, lack adaptability across different hardware platforms and workloads, thereby reducing their robustness and effectiveness. To address these challenges, we present ExpertFlow, a runtime system for MoE inference that combines adaptive expert prefetching and cache-aware routing. ExpertFlow continuously adjusts its prediction horizon for expert activation by leveraging runtime statistics such as transfer bandwidth, parameter dimensionality, and model feedback signals. Furthermore, it incorporates a hybrid cross-layer prediction scheme that fuses pregating information with intermediate computational states to anticipate future expert needs. By adaptively refining prefetching decisions and aligning them with actual usage behavior, ExpertFlow effectively decreases cache misses and removes latency caused by expert swap-ins. Our evaluation demonstrates that ExpertFlow reduces model stall time to less than 0.1% of the baseline, highlighting its capability to optimize MoE inference under stringent memory constraints.