A fully implantable left ventricular assist system comprising a pumping means connectable via adapter elements to the ventricle includes two compressible chambers in the form of sacs (5, 5′) and a compressing means (4) to alternatingly fill and discharge the compressible chambers (5, 5′) at the same time, including a drive unit (41) assigned thereto, a cooling means (50) for cooling the drive unit (41), and a power supply unit (60) for the drive unit (41) and cooling means (50).In this implantable system the pumping means, compression means (4), drive unit (41) and part of the cooling means (50) are accommodated in a two-part housing (1) on which tubular ports (10a, 10b; 10′a, 10′b) for connecting Y-shaped adapter elements (3, 3′) are configured.