We are focusing on the function of the respiratory system, which is the exchange of oxygen and carbon dioxide between the environment and the cells of the body. Set of differential equations systems of the respiratory apparatus is developed based on Bertalanffy’s systems theory, considering that the respiratory apparatus is a so-called hierarchical system. This hierarchical order is broken down into sub-levels because the breathing apparatus also has further subsystems. The respiratory apparatus is working under the control of two levels. Block diagram is developed to demonstrate the kind of goal orientation we want to make effective because this always depends on the current needs of the given organism. A block diagram of the brain-controlled breathing apparatus in case of normal functioning is demonstrated here. A block diagram of the part directed by the hypothetical secondary brain was also recorded. It is also demonstrated that this part of the organization is functioning also under normal circumstances, only the brain activity obscures (masks) the everyday activity of the hypothetical brain. We have emphasized that the breathing apparatus is the first priority for people