This book constitutes the refereed proceedings of the Second International Workshop on Asynchronous Many-Task Systems and Applications, WAMTA 2024, held in Knoxville, TN, USA during February 14-16, 2024. The 11 full papers and 5 short papers included in this book were carefully reviewed and selected from 20 submissions. The WAMTA 2024 proceedings help developers, users, and proponents of these models and systems share experience, discuss how they meet the challenges posed by Exascale system architectures, and explore opportunities for increased performance, robustness, productivity, and full-system utilization.