The existing discrete architecture graph neural networks (GNNs) are unable to extract deep spatiotemporal representations, the single variable dependencies in existing GNNs tend to learn a single type of time scale pattern, and fixed graph structures in existing GNNs cannot accurately represent the entire degradation process of aeroengine performance, resulting in poor prediction accuracy in predicting remaining useful life (RUL) of aeroengines. To address these issues, a novel GNN named multi scale dynamic graph neural ordinary differential equations (MDGODE) is proposed for RUL prediction of aeroengines. In MDGODE, a multi-scale framework is first established to capture the laten temporal dependence of aeroengine sensor signals at different time scales; secondly, a multi-scale dynamic graph structure learning module is designed to automatically adjust the spatial interaction of different sensor signals and capture the dynamic correlation between sensor signals at different time scales; finally, a new type of spatiotemporal coupled graph neural ordinary differential equations is constructed to capture the deep spatiotemporal representation in the performance degradation data of aeroengines. Due to the above characteristics, the proposed MDGODE has strong spatiotemporal representation capability and robustness to complex non-stationary performance degradation processes of aeroengines. Therefore, the prediction accuracy of MDGODE for aeroengine RUL is significantly improved compared to existing mainstream aeroengine RUL prediction methods. The proposed RUL prediction method based on MDGODE achieves a root mean square error (RMSE) of 14.06 and a Score of 879.36 for the RUL prediction values corresponding to the test set of FD004 subset in the aeroengine performance degradation dataset C-MAPSS. This experimental result verifies the effectiveness and superiority of the proposed method.