Title: Asynchronous Message Passing: A new Framework for Learning in Graphs. Abstract: This paper studies asynchronous message passing (AMP), a new framework for applying neural networks to graphs. Existing graph neural networks (GNNs) use the message passing framework which is based on the synchronous distributed computing model. In traditional GNNs, nodes aggregate their neighbors in each round, which causes problems such as oversmoothing and expressiveness limitations. On the other hand, our AMP framework is based on the \textit{asynchronous} model, where nodes react to messages of their neighbors individually. We prove (i)  AMP is at least as powerful as the message passing framework, (ii) AMP is more powerful than the $1-$WL test for graph isomorphism, an important benchmark for message passing GNNs, and (iii) conceptually, AMP can even separate any pair of graphs and compute graph isomorphism. We experimentally validate the findings on AMP's expressiveness, and show that AMP might be better suited to propagate messages over large distances in graphs. We also demonstrate that AMP performs well on several graph classification benchmarks.