Sounds caused by the action of the heart reflect both its health as well as deficiencies and are examined by physicians since antiquity. Pathologies of the valves, e.g. insufficiencies and stenosis, cardiac effusion, arrhythmia, inflammation of the surrounding tissue and other diagnosis can be reached by experienced physicians. However, practice is needed to assess the findings correctly. Furthermore, stethoscopes do not allow for long-term monitoring of a patient. Recently, radar technology has shown the ability to perform continuous touchless and thereby burden-free heart sound measurements. In order to perform automated classification of the signals, the first and most important step is to segment the heart sounds into their physiological phases. This paper examines the use of different Long Short-Term Memory (LSTM) architectures for this purpose based on a large dataset of radar-recorded heart sounds gathered from 30 different test persons in a clinical study. The best-performing network, a bidirectional LSTM, achieves a sample-wise accuracy of 93.4 % and a F1 score for the first heart sound of 95.8 %.