Abstract. Planetary reducers have a wide and significant application in modern machine industry. They are extremely compact and reliable, and they can achieve a wide range of gear ratios as well as high efficiency. Since they often operate in extremely changeable working conditions, such as often starting and stoping, it is both interesting and desirable to study their dynamic behaviour. This paper presents a dynamic model of a planetary reducer with double planet gears created by applying Lagrange's equations of the second kind. After a planetary gear reducer has been designed and a CAD model created, the dynamic model was made. Most of characteristic values needed for solution of the equations are taken from the CAD model. Due to their complexity, the equations are solved in math simulation software. A lot of interesting results concerning the dynamic behaviour of the model are obtained, which can be helpful in understanding the dynamic occurrences in the inside of a planetary gearbox. At the end of the paper, conclusions are drawn, and further research directions in this area are given.