Abstract <p>Breast cancer is one of the most common and dangerous types of cancer in women. Modern approaches to detect and treat it early increasingly use methods of artificial intelligence and deep learning. In this paper we study breast histopathological images using transformer neural networks and deep neural networks. The vision transformer (ViT) and data efficient image transformer (DeiT) models are used as the transformer models. ResNet50, VGG16, DenseNet201, EfficientNet-B7, and Xception are chosen as models of deep convolutional neural networks (CNNs). All models are pretrained on the ImageNet1k image set and then further trained on a set of 4356 histopathological images. The results of computer experiments show that the EfficientNet-B7 model outperform the other models, achieving an accuracy rate of 95.84%. In order to improve the performance of histopathological image classification models, a knowledge distillation method is applied in this work, which allows obtaining a new deep neural network model DeiT_ B_dist for a precise classification of histopathological images and breast cancer detection. Its accuracy is 98.14%, it outperforms the other models, and its accuracy is comparable to the results of other researchers.</p>