Hemo(dia)filtration apparatus comprising: - a blood treatment device having a first chamber, a second chamber and a semipermeable membrane that separates said first chamber from said second chamber, said first chamber having at least one first opening and one second opening; - a single needle extracorporeal blood circuit comprising a first line connected to said first opening and a second line connected to said second opening; - a fluid circuit having at least one exit line to withdraw spent fluid from said second chamber; - at least one infusion line (11; 12) which flows into said first line and/or said second line to infuse a substitution fluid; - a first pump arranged to generate a first flow rate of fluid in said blood circuit; - a second pump (13; 14) arranged to generate a second flow rate of substitution fluid in said infusion line (11; 12); - ultrafiltration means arranged to generate a third flow rate of ultrafiltration from said first chamber to said second chamber through said semipermeable membrane; - control means arranged to control said first pump, said second pump (13; 14) and said ultrafiltration means, said control means comprising means for performing withdrawal arterial phases alternated with return venous phases, characterized in that: * in at least one arterial phase, the third flow rate QF A of ultrafiltration is less than the first flow rate QB A of fluid and greater than the second flow rate QS A of substitution fluid, having thereby a flow rate QF A -QS A of withdrawal from patient; * in at least one venous phase, the third flow rate QF V of ultrafiltration is greater than zero and less than both the first flow rate QB V of fluid and the second flow rate QS V of substitution fluid, having thereby a flow rate QS V -QF V of return to the patient. - a blood treatment device having a first chamber, a second chamber and a semipermeable membrane that separates said first chamber from said second chamber, said first chamber having at least one first opening and one second opening; - a single needle extracorporeal blood circuit comprising a first line connected to said first opening and a second line connected to said second opening; - a fluid circuit having at least one exit line to withdraw spent fluid from said second chamber; - at least one infusion line (11; 12) which flows into said first line and/or said second line to infuse a substitution fluid; - a first pump arranged to generate a first flow rate of fluid in said blood circuit; - a second pump (13; 14) arranged to generate a second flow rate of substitution fluid in said infusion line (11; 12); - ultrafiltration means arranged to generate a third flow rate of ultrafiltration from said first chamber to said second chamber through said semipermeable membrane; - control means arranged to control said first pump, said second pump (13; 14) and said ultrafiltration means, said control means comprising means for performing withdrawal arterial phases alternated with return venous phases, characterized in that: * in at least one arterial phase, the third flow rate QF A of ultrafiltration is less than the first flow rate QB A of fluid and greater than the second flow rate QS A of substitution fluid, having thereby a flow rate QF A -QS A of withdrawal from patient; * in at least one venous phase, the third flow rate QF V of ultrafiltration is greater than zero and less than both the first flow rate QB V of fluid and the second flow rate QS V of substitution fluid, having thereby a flow rate QS V -QF V of return to the patient. * in at least one arterial phase, the third flow rate QF A of ultrafiltration is less than the first flow rate QB A of fluid and greater than the second flow rate QS A of substitution fluid, having thereby a flow rate QF A -QS A of withdrawal from patient; * in at least one venous phase, the third flow rate QF V of ultrafiltration is greater than zero and less than both the first flow rate QB V of fluid and the second flow rate QS V of substitution fluid, having thereby a flow rate QS V -QF V of return to the patient.