The paper proposes two approaches to solving the problem of determining the breed of dogs and cats in images. The first one is a one-step classification without previously determining the species of the animal. The second one consists of two steps - in the first one the image is classified based on the species, while in the second one the image is passed to a specialized classifier which determines the breed within the previously determined species. Both solutions are based on the use of convolutional neural networks, as well as the data augmentation technique. Additionally, the impact of the application of the active learning technique was analyzed for both proposed solutions.