An automatic toothed variable-speed gearbox is provided, comprising two or more stages of planetary mechanisms, wherein each stage of planetary mechanisms comprises sun gears, a carrier gear and planetary gears, which can be optionally bilateral. The planetary mechanisms comprise two or more power-transfer flows. In one embodiment, the carrier gear of the first stage can be integrated with the sun wheel gear of the second stage, wherein the sun wheel gear of the first stage can be integrated with the carrier gear of the second stage, wherein the transmission ratio is changed without disengaging gears and without using control devices by initially stopping at least one gear in a stop position or in a position adjacent to the stop position, depending on equality or closeness of forces which are originated from different power flows, and which are opposite in terms of orientation, and which are applied thereto from different sides and from main power flow gears split by gears of the cinematic chains, wherein the forces are further determined by the load, ratio between diameters of the gears, center-to-center distances, which are further determined by quantity of teeth thereof and by pitch modules, and due to movability of said gear which is determined by change in load, forces, the gears' circular and relative velocities in such a way that such an equality is reestablished due to the tendency of the forces to balance and to set the gears into the initial balanced position.