Four-wheel drive system

The invention relates to a four-wheel drive system and an electric drive system for a four-wheel drive vehicle which improve running performance of an automotive vehicle by inhibiting a driving torque from becoming insufficient upon occurrence of a slip. A R slip sensing means (137) of a DC-motor-torque calculating means (139) senses a slip due to a spin of rear wheels (15R, 15L). When the rear wheel slip is sensed, an R slip DC-motor-torque correcting means (139) corrects a torque of the rear wheels (15R, 15L) so that a driving force of the rear wheels (15R, 15L) is reduced and then increased. The R slip DC-motor-torque correcting means (139) reduces a driving torque of the rear wheels (15R, 15L) to eliminate the slip and holds the reduced driving torque until the slip is eliminated, and then increases the driving torque to a value lower than a value which the driving torque has taken at the time of occurrence of the slip. The driving torque is increased to a predetermined limit value depending on the number of slips.