Title: Towards predicting dynamic stability of power grids with Graph Neural Networks. Abstract: To mitigate climate change, the share of renewable energies in power production needs to be increased. Renewables introduce new challenges to power grids regarding the dynamic stability due to decentralization, reduced inertia and volatility in production. However, dynamic stability simulations are intractable and exceedingly expensive for large grids. Graph Neural Networks (GNNs) are a promising method to reduce the computational effort of analyzing dynamic stability of power grids. We provide new datasets of dynamic stability of synthetic power grids and find that GNNs are surprisingly effective at predicting highly non-linear targets from topological information only. We show that large GNNs outperform GNNs from previous work as well as as handcrafted graph features and semi-analytic approximations. Further, we demonstrate GNNs can accurately identify \emph{trouble maker}-nodes in the power grids. Lastly, we show that GNNs trained on small grids can perform accurately on a large synthetic Texan power grid model, which illustrates the potential of our approach.