The article proposes a multi-camera tracking system for an object, implemented using computer vision technologies and allowing the video surveillance operator in real time to select an object that will be monitored by the system in future. It will be ready to give out the location of the object at any time. The solution to this problem is divided into three main stages: the detection stage, the tracking stage and the stage of interaction of several cameras. Methods of detection, tracking of objects and the interaction of several cameras have been investigated. To solve the problem of detection, the method of optical flow and the method of removing the background were investigated, to solve the problem of tracking — the method of matching key points and the correlation method, to solve the problem of interaction between several surveillance cameras — the method of the topological graph of a network of cameras. An approach is proposed for constructing a system that uses a combination of the background removal method, the correlation method and the method of the topological graph of a network of cameras. The stages of detection and tracking have been experimentally implemented, that is, the task of tracking an object within the coverage area of one video camera has been solved. The implemented system showed good results: a sufficiently high speed and accuracy with rare losses of the tracked object and with a slight decrease in the frame rate.