Apparatus for blood treatment for single-needle operation, comprising: blood collection means which comprise a sealed volume; gas storage means which comprise a sealed volume; means (19, 21) for making a connection between the blood collection means and the gas storage means, the blood collection means and the gas storage means forming, together with the means (19, 21) for making a connection between the blood collection means and the gas storage means, a sealed volume, which no gas can enter and from which no gas can exit; means for feeding blood to the blood collection means in an extracorporeal blood circuit, the extracorporeal blood circuit having a blood infeed line which runs to an inlet of a blood treatment unit and a blood return line which leads away from an outlet of the blood treatment unit; gas compression means; and a control and arithmetic unit which co-operates with the blood collection means, the gas storage means, the means (19, 21) for making a connection between the blood collection means and the gas storage means, and the gas compression means such that, in an arterial phase when the blood collection means is being filled, gas which is displaced from the blood collection means is transferred to the gas storage means and, in a venous phase for emptying the blood collection means, gas which has been stored in the gas storage means is transferred to the blood collection means by the gas compression means such that blood can be fed to the extracorporeal blood circuit in the arterial phase and discharged from the extracorporeal blood circuit in the venous phase, characterised in that the control and arithmetic unit is configured such that, to initialise the successive arterial and venous phases, a pressure Pair reservoir max which is to be set in the gas storage means is calculated, for the initialisation, the previously calculated pressure p air reservoir max is set in the gas storage means before the arterial and venous phases are started and, once the pressure is set, the arterial and venous phases are started. blood collection means which comprise a sealed volume; gas storage means which comprise a sealed volume; means (19, 21) for making a connection between the blood collection means and the gas storage means, the blood collection means and the gas storage means forming, together with the means (19, 21) for making a connection between the blood collection means and the gas storage means, a sealed volume, which no gas can enter and from which no gas can exit; means for feeding blood to the blood collection means in an extracorporeal blood circuit, the extracorporeal blood circuit having a blood infeed line which runs to an inlet of a blood treatment unit and a blood return line which leads away from an outlet of the blood treatment unit; gas compression means; and a control and arithmetic unit which co-operates with the blood collection means, the gas storage means, the means (19, 21) for making a connection between the blood collection means and the gas storage means, and the gas compression means such that, in an arterial phase when the blood collection means is being filled, gas which is displaced from the blood collection means is transferred to the gas storage means and, in a venous phase for emptying the blood collection means, gas which has been stored in the gas storage means is transferred to the blood collection means by the gas compression means such that blood can be fed to the extracorporeal blood circuit in the arterial phase and discharged from the extracorporeal blood circuit in the venous phase, characterised in that the control and arithmetic unit is configured such that, to initialise the successive arterial and venous phases, a pressure Pair reservoir max which is to be set in the gas storage means is calculated, for the initialisation, the previously calculated pressure p air reservoir max is set in the gas storage means before the arterial and venous phases are started and, once the pressure is set, the arterial and venous phases are started.