This thesis work is set in the context of synthetic protein sequences generation. Starting from a dataset of protein sequences that belong to the same protein family, the goal is to generate new sequences which are statistically indistinguishable from the ones in the same family. This is possible thanks to the recent advance in protein sequencing, which has made available a large number of protein family datasets. To do this, we use neural network generative models that are able to learn the probability distribution of a dataset, so that we can sample from that distribution and generate new synthetic data. In particular, two different kinds of models are proposed: generative adversarial networks (GANs) and autoregressive (AR) neural networks.