A blood processing system for performing hemodialysis on a patient to remove metabolic waste from the patient's blood comprising: a blood processing apparatus (10, 110), a first flow path (16, 126) for fluid communication between the patient and said blood processing apparatus, said blood processing apparatus (10, 110) comprising: spaced apart first inner and first outer generally cylindrical surfaces defining a first gap (28, 130) therebetween, the first flow path (16, 126) communicating with the first gap (28, 130) for flowing blood therethrough; at least one of the first inner and first outer surfaces carrying a filter membrane (46, 132) that allows large molecules to pass therethrough; a collection sink for collecting filtered plasma passing through the filter membrane (46, 132), a drive assembly (44, 120) for causing relative movement between the first inner and first outer surfaces to create movement of the blood within the first gap (28, 130) that induces transport of plasma comprising waste and large molecules through the membrane while substantially preventing the passage of blood cells therethrough to provide filtered plasma comprising waste and large molecules that is substantially reduced of blood cells, spaced apart second inner and second outer generally cylindrical surfaces defining a second gap (76, 150), at least one of the second inner and second outer surfaces carrying a diffusion membrane (70, 148), a second flow path (52, 80, 162) communicating with said second gap (76, 150) for flowing said filtered plasma comprising waste and large molecules into the second gap, a drive assembly (98, 120) causing relative movement between the second inner and outer surfaces to create movement of plasma comprising waste and large molecules within the second gap that induces transport of waste comprising small molecules and medium molecules by diffusion through the diffusion membrane while the passage of said plasma comprising large molecules through the diffusion membrane is substantially prevented. a blood processing apparatus (10, 110), a first flow path (16, 126) for fluid communication between the patient and said blood processing apparatus, said blood processing apparatus (10, 110) comprising: spaced apart first inner and first outer generally cylindrical surfaces defining a first gap (28, 130) therebetween, the first flow path (16, 126) communicating with the first gap (28, 130) for flowing blood therethrough; at least one of the first inner and first outer surfaces carrying a filter membrane (46, 132) that allows large molecules to pass therethrough; a collection sink for collecting filtered plasma passing through the filter membrane (46, 132), a drive assembly (44, 120) for causing relative movement between the first inner and first outer surfaces to create movement of the blood within the first gap (28, 130) that induces transport of plasma comprising waste and large molecules through the membrane while substantially preventing the passage of blood cells therethrough to provide filtered plasma comprising waste and large molecules that is substantially reduced of blood cells, spaced apart second inner and second outer generally cylindrical surfaces defining a second gap (76, 150), at least one of the second inner and second outer surfaces carrying a diffusion membrane (70, 148), a second flow path (52, 80, 162) communicating with said second gap (76, 150) for flowing said filtered plasma comprising waste and large molecules into the second gap, a drive assembly (98, 120) causing relative movement between the second inner and outer surfaces to create movement of plasma comprising waste and large molecules within the second gap that induces transport of waste comprising small molecules and medium molecules by diffusion through the diffusion membrane while the passage of said plasma comprising large molecules through the diffusion membrane is substantially prevented. spaced apart first inner and first outer generally cylindrical surfaces defining a first gap (28, 130) therebetween, the first flow path (16, 126) communicating with the first gap (28, 130) for flowing blood therethrough; at least one of the first inner and first outer surfaces carrying a filter membrane (46, 132) that allows large molecules to pass therethrough; a collection sink for collecting filtered plasma passing through the filter membrane (46, 132), a drive assembly (44, 120) for causing relative movement between the first inner and first outer surfaces to create movement of the blood within the first gap (28, 130) that induces transport of plasma comprising waste and large molecules through the membrane while substantially preventing the passage of blood cells therethrough to provide filtered plasma comprising waste and large molecules that is substantially reduced of blood cells, spaced apart second inner and second outer generally cylindrical surfaces defining a second gap (76, 150), at least one of the second inner and second outer surfaces carrying a diffusion membrane (70, 148), a second flow path (52, 80, 162) communicating with said second gap (76, 150) for flowing said filtered plasma comprising waste and large molecules into the second gap, a drive assembly (98, 120) causing relative movement between the second inner and outer surfaces to create movement of plasma comprising waste and large molecules within the second gap that induces transport of waste comprising small molecules and medium molecules by diffusion through the diffusion membrane while the passage of said plasma comprising large molecules through the diffusion membrane is substantially prevented.