This invention relates to a shift control of a continuously variable transmission having an auxiliary transmission when a vehicle runs on a slope road. 
A continuously variable transmission including a continuously variable transmission mechanism (variator) and an auxiliary transmission mechanism arranged to selectively switch a plurality of forward shift stages has been known.  In this transmission, it is possible to enlarge shift region by the auxiliary transmission mechanism relative to a continuously variable transmission constituted only by the variator.  Accordingly, it is possible to improve efficiency of an engine, and to improve fuel consumption. 
In this transmission, when the shift is performed together with the shift of the auxiliary transmission mechanism, the variator is shifted in a direction opposite to the shift direction of the auxiliary transmission mechanism when the shift of the auxiliary transmission mechanism is started.  With this, the transmission ratios of the entire transmission before and after the shift are not varied.  The variation of the rotational speed of the engine is suppressed, and accordingly it is possible to suppress shift shock (Japanese Patent Application Publication No.  5-79554). 
Moreover, U.S. Pat.  No.  4,823,646 (corresponding to Japanese Patent Application Publication No.  62-216831) discloses a transmission arranged to prohibit an upshift for preventing a shift busy and for ensuring a driving force when a running resistance is larger than an engine output when a vehicle runs on a slope road such as a climbing road.