This paper presents a study of the dynamic (recurrent) quadratic neural unit (QNU) -a class of higher order network or a class of polynomial neural network- as applied to the prediction of lung respiration dynamics. Human lung motion during respiration features nonlinear dynamics and displays quasiperiodical or even chaotic behavior. An attractive approximation capability of the recurrent QNU are demonstrated on a long term prediction of time series generated by chaotic MacKey-Glass equation, by another highly nonlinear periodic time series, and on real lung motion measured during patients respiration. The real time recurrent learning (RTRL) rule is derived for dynamic QNU in a matrix form that is also efficient for implementation. It is shown that the standalone QNU gives promising results on a longer prediction times of the lung position compared to results in recent literature. In the end, we show even more precise results of two QNUs implemented as two local nonlinear predictive models and thus we present and discus a promising direction for high precision prediction of lung motion.