GAN framework may be used with almost any kind of neural networks. Take a look at this papers for example:

Continuous recurrent neural networks with adversarial training https://arxiv.org/abs/1611.09904 7

Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs https://arxiv.org/abs/1706.02633 11

Language Generation with Recurrent Generative Adversarial Networks without Pre-training https://arxiv.org/abs/1706.01399 3

Contextual RNN-GANs for Abstract Reasoning Diagram Generation https://arxiv.org/abs/1609.09444 5