Recent research on Deep Graph Networks (DGNs) has broadened the domain of learning on graphs to real-world systems of interconnected entities that evolve over time. This paper addresses prediction problems on graphs defined by a stream of events, possibly irregularly sampled over time, generally referred to as Continuous-Time Dynamic Graphs (C-TDGs). While many predictive problems on graphs may require capturing interactions between nodes at different distances, existing DGNs for C-TDGs are not designed to propagate and preserve long-range information - resulting in suboptimal performance. In this work, we present Continuous-Time Graph Anti-Symmetric Network (CTAN), a DGN for C-TDGs designed within the ordinary differential equations framework that enables efficient propagation of long-range dependencies. We show that our method robustly performs stable and non-dissipative information propagation over dynamically evolving graphs, where the number of ODE discretization steps allows scaling the propagation range.We empirically validate the proposed approach on several real and synthetic graph benchmarks, showing that CTAN leads to improved performance while enabling the propagation of long-range information.