One of the main ways to improve fuel economy of vehicles is to provide operation of the engine in a narrow range with the best efficiency. The number of speeds in modern automatic transmissions has significantly increased for this reason. Obviously, an increase in the number of speeds leads to an increase in the number of gears and shifting elements, transmission complication and an increase in overall dimensions and weight. The article discusses the planetary-layshaft transmission, which has parallel connection of two differentials and three sets of gears with fixed axles of wheels. Transmissions of such arrangement allow to transmit the power in parallel by three flows from the input shaft to the output one and provide a significantly larger number of speeds with fewer gears and shifting elements, due to combinations of different operating modes of the differentials. Applying of planetary-layshaft transmissions limits the presence of double and triple transition shifts between adjacent speeds, when two or three pairs of control elements (clutches or brakes) are simultaneously switching off and on during gearshift. The purpose of the article is to find a sequence of single transition shifts for a planetary-layshaft transmission and to calculate the gear ratios that provide a set of speed ratios close to the given.