In recent years, the use of electroencephalography (EEG) for the clinical diagnosis of neurodegenerative diseases, such as Alzheimer’s disease, frontotemporal dementia and dementia with Lewy bodies, has been extensively studied. The classification of these different neurodegenerative diseases can benefit from machine learning techniques which, compared to manual diagnosis methods, have higher reliability and higher recognition performance, being able to handle large amounts of data. The purpose of this work is to develop an automatic classification method that can recognize a number of different neurodegenerative diseases such the aforementioned ones, having similar corresponding EEGs or being difficult to discern by inspection from a human operator. We show how a recurrent neural network (RNN) based on long short-term memory (LSTM) elements can successfully perform the task of classification, when the data are properly pre-processed.