A device for feeding a converting unit with a web substrate, the converting unit converting the substrate when stopped. The device includes a main drive roller rotating on a main shaft a main electric drive motor (14) rotating (T) the main roller (12), a satellite roller oscillating about the main roller (12), between upstream and downstream on the path of a substrate. Two lateral levers secured to the main shaft hold the satellite roller and are mounted on the main shaft. The substrate is maintained between the main and satellite rollers to change cyclically between a constant speed to a zero speed at the exit side of the satellite roller. At least one secondary electric drive motor oscillates the main shaft, the two lateral levers and the satellite roller.