The invention mainly relates to a power transmission device (1) between an internal combustion engine (2) and vehicle wheels (3) consisting of a pair of electrical machines (4.1, 4.2) and a mechanical assembly (90), wherein said assembly (90) comprises at least two epicycloidal trains (5, 9) each of which is provided with three mutually engageable elements. According to said invention, a switching device (23.1) comprises means (23, 28) for simultaneously connecting the machine shaft (11) to two other elements (11.1, 11.2) of the mechanical assembly (90) during switching between two operating modes of the transmission device (1).