Sleep-related breathing disorders have severe impact on the quality of lives of those suffering from them. These disorders present with a variety of symptoms, out of which snoring and groaning are very common. This paper presents an algorithm to identify and classify segments of acoustic respiratory sound recordings that contain both groaning and snoring events. The recordings were obtained from a database containing 20 subjects from which features based on the Mel-frequency cepstral coefficients (MFCC) were extracted. In the first stage of the algorithm, segments of recordings consisting of either snoring or groaning episodes - without classifying them - were identified. In the second stage, these segments were further differentiated into individual groaning or snoring events. The algorithm in the first stage achieved a sensitivity and specificity of 90.5% ±2.9% and 90.0% ±1.6% respectively, using a RUSBoost model. In the second stage, a random forest classifier was used, and the accuracies for groan and snore events were 78.1% ±4.7% and 78.4% ±4.7% respectively.