This work aims to classify sleep stages based on tachograms using Convolutional Neural Networks (CNNs) and investigate advantages of specialized classifiers. The tachograms of 5422 patients were extracted from the Sleep Heart Health Study. A CNN was trained to classify each 30 s epoch into four distinct sleep stages. The patients were divided into four subgroups by Apnoe-Hypopnoe-Index (AHI). From each subgroup, 20 % of pa-tients were held out as test data. One general model was trained on all training patients and four narrowed models were each trained on one subgroup. Furthermore, the general model was retrained on the subgroups, yielding four additional transfer learning models. Our general model gained an average Cohen's Kappa score of 0.53. The general model outperformed the narrowed models on each test subset. From the narrowed models, training on the subgroup with AHI 5-15 achieved best overall performance. However, a correlation exists between the size of train sets and classification quality. Transfer learning did not improve the results. CNN models are capable of learning features from tachograms with very good classification performance compared to other works using heart rate only. However, the pursued strategies for specializing classifiers did not yield any advantages over our general model.