Large language models typically generate tokens autoregressively, using each token as input for the next. Recent work on Speculative Decoding has sought to accelerate this process by employing a smaller, faster draft model to more quickly generate candidate tokens. These candidates are then verified in parallel by the larger (original) verify model, resulting in overall speedup compared to using the larger model by itself in an autoregressive fashion. In this work, we introduce AMUSD (Asynchronous Multi-device Speculative Decoding), a system that further accelerates generation by decoupling the draft and verify phases into a continuous, asynchronous approach. Unlike conventional speculative decoding, where only one model (draft or verify) performs token generation at a time, AMUSD enables both models to perform predictions independently on separate devices (e.g., GPUs). We evaluate our approach over multiple datasets and show that AMUSD achieves an average 29% improvement over speculative decoding and up to 1.96$\times$ speedup over conventional autoregressive decoding, while achieving identical output quality. Our system is open-source and available at https://github.com/BradMcDanel/AMUSD/.