a variable cylinder device for internal combustion engines having a movable rocker arm and a movable rocker shaft in which an oil - supplying type lash adjuster is fitted to a housing having a main oil - passage and the rocker shaft is secured to a rocker support . oil for lubricating the sliding surface of movable rocker shaft is supplied from the main oil - passage through a series of passages formed in the housing and the rocker support , especially through a pipe protruding from the rocker support and slidably inserted into the housing . the housing is further provided with a mechanism for reducing the oil - pressure in the main oil - passage and a mechanism for preventing rotation of the rocker support .