In this paper, we propose a method for class-incremental learning of potentially overlapping sounds for solving a sequence of multi-label audio classification tasks. We design an incremental learner that learns new classes independently of the old classes. To preserve knowledge about the old classes, we propose a cosine similarity-based distillation loss that minimizes discrepancy in the feature representations of subsequent learners, and use it along with a Kullback-Leibler divergence-based distillation loss that minimizes discrepancy in their respective outputs. Experiments are performed on a dataset with 50 sound classes, with an initial classification task containing 30 base classes and 4 incremental phases of 5 classes each. After each phase, the system is tested for multi-label classification with the entire set of classes learned so far. The proposed method obtains an average F1-score of 40.9% over the five phases, ranging from 45.2% in phase 0 on 30 classes, to 36.3% in phase 4 on 50 classes. Average performance degradation over incremental phases is only 0.7 percentage points from the initial F1-score of 45.2%.