Although rare diseases are characterized by low prevalence, approximately 300 million people are affected by a rare disease. The early and accurate diagnosis of these conditions is a major challenge for general practitioners, who do not have enough knowledge to identify them. In addition to this, rare diseases usually show a wide variety of manifestations, which might make the diagnosis even more difficult. A delayed diagnosis can negatively affect the patient's life. Therefore, there is an urgent need to increase the scientific and medical knowledge about rare diseases. Natural Language Processing (NLP) and Deep Learning can help to extract relevant information about rare diseases to facilitate their diagnosis and treatments. The paper explores the use of several deep learning techniques such as Bidirectional Long Short Term Memory (BiLSTM) networks or deep contextualized word representations based on Bidirectional Encoder Representations from Transformers (BERT) to recognize rare diseases and their clinical manifestations (signs and symptoms) in the RareDis corpus. This corpus contains more than 5,000 rare diseases and almost 6,000 clinical manifestations. BioBERT, a domain-specific language representation based on BERT and trained on biomedical corpora, obtains the best results. In particular, this model obtains an F1-score of 85.2% for rare diseases, outperforming all the other models.