Generative adversarial networks (GANs) are recently highly successful in generative applications involving images and start being applied to time series data. Here we describe EEG-GAN as a framework to generate electroencephalographic (EEG) brain signals. We introduce a modification to the improved training of Wasserstein GANs to stabilize training and investigate a range of architectural choices critical for time series generation (most notably up- and down-sampling). For evaluation we consider and compare different metrics such as Inception score, Frechet inception distance and sliced Wasserstein distance, together showing that our EEG-GAN framework generated naturalistic EEG examples. It thus opens up a range of new generative application scenarios in the neuroscientific and neurological context, such as data augmentation in brain-computer interfacing tasks, EEG super-sampling, or restoration of corrupted data segments. The possibility to generate signals of a certain class and/or with specific properties may also open a new avenue for research into the underlying structure of brain signals.