In a hydro-mechanical transmission for automobiles which has an input shaft, an output shaft, a differential gear set including an input element connected to the input shaft and an output element connected to the output shaft and two reaction elements, a first positive displacement hydraulic pump-motor connected to the input shaft, a second hydraulic pump-motor connected to the first hydraulic pump-motor through a pair of conduits, a first clutch for performing the low operational mode of the low speed ratio by connecting the second hydraulic pump-motor to one of the two reaction elements, and a second clutch for performing the high operational mode of the high speed ratio by connecting the second hydraulic pump-motor to the other reaction element, the operational modes being switched over when the rotational speed of the first clutch corresponds to or is synchronized with that of the second clutch, the improvement being, whether a setting signal is generated for increasing or decreasing the speed ratio, the signal is detected simultaneously with the correspondence of the rotational speed of each clutch, and upon correspondence thereof, the clutches are operated so as to perform the high operational mode when the setting signal is for increasing the speed ratio and to perform the low operational mode when the setting signal is for decreasing the speed ratio.