A transmission system for a vehicle comprising: a. a torque converter which includes: ▪ an input for connection to a driving shaft, the input of the converter being formed by a support hub of a casing of the converter on which a pump of the converter is supported; and ▪ an output hydraulically connected to the input via a turbine of the converter driven by the pump; b. an output shaft and an input shaft of the converter; c. a gearbox which can be connected to the driving wheels of the vehicle; d. a selective connection member for selectively transmitting the motion of the input shaft to the output shaft or allowing the independent rotation of the input and output shafts (2, 3); wherein: ▪ the output shaft is: - rigidly connected to the output of the torque converter; - connected to the gearbox by means of at least one output gear (21a, b); and ▪ the input shaft: - is rigidly connected to the input of the torque converter; - is coaxial with the output shaft and positioned inside this shaft in a cavity therein; and - has a further output for connection to a service pump of the vehicle; wherein there are formed on the input shaft a first end and a second end axially opposite the first end, each end projecting in an axial direction relative to respective ends (20a, b) of the output shaft; wherein the output shaft comprises at least one output gear (21a, b) disposed in a longitudinally intermediate position between the selective connection member and the converter, characterized by a mechanical damper interposed between the input shaft and the output shaft and interacting with the selective connection member; wherein the first end is connected to the support hub of the converter, while the mechanical damper is keyed on to the second end. a. a torque converter which includes: ▪ an input for connection to a driving shaft, the input of the converter being formed by a support hub of a casing of the converter on which a pump of the converter is supported; and ▪ an output hydraulically connected to the input via a turbine of the converter driven by the pump; ▪ an input for connection to a driving shaft, the input of the converter being formed by a support hub of a casing of the converter on which a pump of the converter is supported; and ▪ an output hydraulically connected to the input via a turbine of the converter driven by the pump; b. an output shaft and an input shaft of the converter; c. a gearbox which can be connected to the driving wheels of the vehicle; d. a selective connection member for selectively transmitting the motion of the input shaft to the output shaft or allowing the independent rotation of the input and output shafts (2, 3); wherein: ▪ the output shaft is: - rigidly connected to the output of the torque converter; - connected to the gearbox by means of at least one output gear (21a, b); and ▪ the input shaft: - is rigidly connected to the input of the torque converter; - is coaxial with the output shaft and positioned inside this shaft in a cavity therein; and - has a further output for connection to a service pump of the vehicle; wherein there are formed on the input shaft a first end and a second end axially opposite the first end, each end projecting in an axial direction relative to respective ends (20a, b) of the output shaft; wherein the output shaft comprises at least one output gear (21a, b) disposed in a longitudinally intermediate position between the selective connection member and the converter, characterized by a mechanical damper interposed between the input shaft and the output shaft and interacting with the selective connection member; wherein the first end is connected to the support hub of the converter, while the mechanical damper is keyed on to the second end. ▪ the output shaft is: - rigidly connected to the output of the torque converter; - connected to the gearbox by means of at least one output gear (21a, b); and - rigidly connected to the output of the torque converter; - connected to the gearbox by means of at least one output gear (21a, b); and ▪ the input shaft: - is rigidly connected to the input of the torque converter; - is coaxial with the output shaft and positioned inside this shaft in a cavity therein; and - has a further output for connection to a service pump of the vehicle; - is rigidly connected to the input of the torque converter; - is coaxial with the output shaft and positioned inside this shaft in a cavity therein; and - has a further output for connection to a service pump of the vehicle;