A marine transmission provides first and second drive gears that have first and second driving surfaces in contact with first and second quantities of rheological fluid. First and second driven surfaces of a propeller shaft are also in contact with the rheological fluids within first and second cavities. Torque is transmitted between the drive gears and the propeller shaft through the increase in viscosity of the rheological fluid. A dog clutch can also be provided in order to lock the propeller shaft to the driving one of the first and second drive gears after the rheological fluid is used to spin up the propeller shaft to the appropriate speed.