Transmission system for a vehicle having an input arranged for connection to a drive source, and an output arranged for connection to a load. The transmission includes a transmission. The transmission includes first input shaft, a first output shaft connected to the output, and a first speed transforming gear connecting the first input shaft and the first output shaft, and a second input shaft, a second output shaft connected to the output, and a second speed transforming gear connecting the second input shaft and the second output shaft. The transmission includes a first coupling member, arranged for coupling the input to the first input shaft at a first speed ratio and a second coupling member, arranged for coupling the input to the second input shaft at a second speed ratio. The first and second speed transforming gears together include a plurality of transmission gears, wherein the transmission gears are arranged such that successive shifting through respective first, second, third, fourth, fifth and sixth gears is effected by alternatingly engaging the first coupling member and the second coupling member.