Title: Memory Learning of Multivariate Asynchronous Time Series. Abstract: Sequential observations from complex systems are usually collected irregularly and asynchronously across variables. Besides, they are typically both serially and cross-sectionally dependent. Recurrent networks are always used to model such sequential data, trying to simultaneously capture marginal dynamics and dependence dynamics with one shared memory. This leads to two problems. First, some heterogeneous marginal information is difficult to be preserved in the shared memory. Second, in an asynchronous setting, missing values across variables will introduce bias in the shared memory. To solve these problems, this paper designs a new architecture that seamlessly integrates continuous-time ODE solvers with a set of memory-aware GRU blocks. It learns memory profiles separately and addresses the issue of asynchronous observations. Numerical results confirm that this new architecture outperforms a variety of state-of-the-art baseline models on datasets from various fields.