Neurodegenerative diseases severely impact the life of millions of patients worldwide, and their occurrence is more and more increasing proportionally to longer life expectancy. Electroencephalography has become an important diagnostic tool for these diseases, due to its relatively simple procedure, but it requires analyzing a large number of data, often carrying a small fraction of informative content. For this reason, machine learning tools have gained a considerable relevance as an aid to classify potential signs of a specific disease, especially in its early stages, when treatments can be more effective. In this work, long short-term memory-based neural networks with different numbers of units were properly designed and trained after accurate data pre-processing, in order to perform a multi-class detection. To this end, a custom dataset of EEG recordings from subjects affected by five neurodegenerative diseases (Alzheimer’s disease, frontotemporal dementia, dementia with Lewy bodies, progressive supranuclear palsy, and vascular dementia) was acquired. Experimental results show that an accuracy up to 98% was achieved with data belonging to different classes of disease, up to six including the control group, while not requiring particularly heavy computational resources.