A method of controlling a power transmitting system for an automotive vehicle, including a continuously variable transmission having an input shaft operatively connected to an engine of the vehicle, and further including an auxiliary transmission which is connected to the continuously variable transmission and which is automatically shifted from one of at least two forward drive positions thereof to another depending upon operating conditions of the vehicle, said power transmitting system being provided with a selector device for selecting an operating mode of said auxiliary transmission, said selector device having an engine brake position for shifting down said auxiliary transmission from one of said at least two forward drive positions to another lower than said one drive position, said method comprising the steps of:
- preparing a plurality of relationships of at least two variables which includes a target speed of said input shaft of said continuously variable transmission, and a currently required output of the engine, said plurality of relationships corresponding to said at least two forward drive positions of said auxiliary transmission, and being determined so that when said auxiliary transmission is shifted down from one of said at least two forward drive positions to said another of said two forward drive positions an actual speed of said engine does not exceed a predetermined maximum permissible speed after the auxiliary transmission is placed in said another of said at least two forward drive positions;
- checking if said selector device is placed in said engine brake position;
- if said selector deviced is placed in said engine brake position, detecting currently selected one of said at least two forward drive positions of said auxiliary transmission;
- selecting one of said plurality of relationships which corresponds to the detected currently selected forward drive position of said auxiliary transmission;
- determining the target speed of said input shaft of said continuously variable transmission, according to the selected one of said plurality of relationships;
- and
- controlling a speed ratio of said continuously variable transmission so that an actual speed of said input shaft coincides with the determined target speed.