A catheter system is provided for accessing the coronary ostia (176, 180) transluminal from a peripheral arterial access site, such as the femoral artery, and for inducing cardioplegia arrest by direct infusion of cardioplegia solution into the coronary arteries. In a first embodiment, the catheter system is in the form of a single perfusion catheter (20) with multiple distal branches (24, 26, 28) for engaging the coronary ostia (176, 180). In a second embodiment, multiple perfusion catheters (82, 84) are delivered to the coronary ostia (176, 180) through a single arterial cannula (104). In a third embodiment, multiple perfusion catheters (112, 114, 116) are delivered to the coronary ostia (176, 180) through a single guiding catheter (126). In a fourth embodiment, multiple catheters (140, 142, 144) are delivered to the coronary ostia (176, 180) through a single guiding catheter (130) which has distal exit ports (134, 136, 138) that are arranged to direct the perfusion catheters into the coronary ostia (176, 180). In each embodiment, the catheters (20) are equipped with an occlusion means (30, 50) at the distal end of the catheter (20) for closing the coronary ostia (176, 180), and isolating the coronary arteries from the systemic blood flow.