Peculiarities of the use of competing cellular automata for problems of recognition of complex captcha systems have been explored. For this purpose, the concept of competing cellular automata has been introduced and a mathematical model of their functioning and interaction has been developed. The mathematical model of competing cellular automata based on the set theory has been described to specify moving cellular automata, which shift to the neighboring states of characters and implement their transition rules in such a way. Based on this mathematical model, a recognition system for captcha images implemented in the code by means of JavaFX 2.0 technology has been developed, which allowed reaching the crossplatformness and correct functioning on different operating systems. The libraries of cellular automata have been developed for the English language. Each symbol of the alphabet is represented in the form of a state system, which is aligned with a cellular automaton with states describing the given symbol. We used Java programming language for development and OpenCV library for the ability to handle images which allowed us to achieve high-quality recognition results. The architecture of the developed system of recognition of complex captcha images in the form of diagrams of classes of the main blocks with detailed descriptions of each class has been considered. Computer experiments have been carried out with different sets of distorted characters used in actual captcha systems and recognition quality indices of the developed software obtained. It has been shown that the probability of obtaining the correct result of captcha image recognition exceeds 80 % with a degree of deformation of characters up to 20 %. With a degree of deformation of characters over 30 %, there is a high probability of false character recognition. The advantages of the method of text character recognition based on competing cellular automata include simplicity of rules of engagement, ability to parallelize the process of recognition easily, capability of recognition of distorted and partially overlapping characters that are the basis of modern captcha systems