Spiking neural networks are notoriously hard to train because of their complex dynamics and sparse spiking signals. However, in part due to these properties, spiking neurons possess high computa- tional power and high theoretical energy efficiency. This thesis introduces an online, supervised, and gradient-based learning algorithm for spiking neural networks. It is shown how gradients of temporal signals that influence spiking neurons can be calculated online as an eligibility trace. The trace rep- resents the temporal gradient as a single scalar value and is recursively updated at each consecutive iteration. Moreover, the learning method uses approximate error signals to simplify their calculation and make the error calculation compatible with online learning. In several experiments, it is shown that the algorithm can solve spatial credit assignment problems with short-term temporal dependencies in deep spiking neural networks. Potential approaches for improving the algorithm’s performance on long-term temporal credit assignment problems are also discussed. Besides the research on spiking neural networks, this thesis includes an in-depth literature study on the topics of neuromorphic computing and deep learning, as well as extensive evaluations of several learning algorithms for spiking neural networks