An injection stretch blow molding apparatus has a preform molding section for molding preforms and a blow molding section for blow molding containers from the preforms retaining heat from when the preforms were injection molded. At a location in a path along which the preforms are carried from the preform molding section to the blow molding section there is a discharge guide section for guiding preforms which are not to be carried to the blow molding section off the carrying path. A method wherein preforms are injection molded in preform molding section and these preforms are carried to a blow molding section and containers are blow molded from the preforms retaining heat from when the preforms were injection molded, includes the steps of switching to either a container molding operating mode using the above steps or a preform molding operation mode wherein part way along the preform carrying path leading to the blow molding section, the preforms being molded in the preform molding section are discharged from the carrying path.