Pump device for pumping liquids, comprising a. a centrifugal pump having a radially pumping pump wheel with a hollow centre, wherein the pump, during operation, can at any time be assigned a value of a first operating parameter, b. a detecting device for detecting the first operating parameter, c. a sensor for measuring a second operating parameter, d. and a control unit for controlling the centrifugal pump, said control unit being connected to the pump, to the detecting device for detecting the first operating parameter and to the sensor and moreover being configured such that it controls the operation of the pump and can remove accumulations of gas from the hollow centre of the pump during the liquid-conveying operation of the pump, by o operating the pump, in a first step for removal of gas, such that at least the first operating parameter of the pump is varied over time (t) in such a way that the first operating parameter assumes a series of different predetermined values one after another, • and that meanwhile values of the second operating parameter that are assigned to the values of the first operating parameter are recorded, o determining, in a second step for removal of gas, local and/or global extreme values of the previously recorded values of the second operating parameter, o determining, in a third step for removal of gas, those values (510) of the first operating parameter that are assigned to the previously determined extreme values of the second operating parameter, o operating the pump, in a fourth step for removal of gas, such that it assumes, for a predetermined period of time, one of the values of the first operating parameter that are assigned to the extreme values of the second operating parameter. a. a centrifugal pump having a radially pumping pump wheel with a hollow centre, wherein the pump, during operation, can at any time be assigned a value of a first operating parameter, b. a detecting device for detecting the first operating parameter, c. a sensor for measuring a second operating parameter, d. and a control unit for controlling the centrifugal pump, said control unit being connected to the pump, to the detecting device for detecting the first operating parameter and to the sensor and moreover being configured such that it controls the operation of the pump and can remove accumulations of gas from the hollow centre of the pump during the liquid-conveying operation of the pump, by o operating the pump, in a first step for removal of gas, such that at least the first operating parameter of the pump is varied over time (t) in such a way that the first operating parameter assumes a series of different predetermined values one after another, • and that meanwhile values of the second operating parameter that are assigned to the values of the first operating parameter are recorded, o determining, in a second step for removal of gas, local and/or global extreme values of the previously recorded values of the second operating parameter, o determining, in a third step for removal of gas, those values (510) of the first operating parameter that are assigned to the previously determined extreme values of the second operating parameter, o operating the pump, in a fourth step for removal of gas, such that it assumes, for a predetermined period of time, one of the values of the first operating parameter that are assigned to the extreme values of the second operating parameter. o operating the pump, in a first step for removal of gas, such that at least the first operating parameter of the pump is varied over time (t) in such a way that the first operating parameter assumes a series of different predetermined values one after another, • and that meanwhile values of the second operating parameter that are assigned to the values of the first operating parameter are recorded, • and that meanwhile values of the second operating parameter that are assigned to the values of the first operating parameter are recorded, o determining, in a second step for removal of gas, local and/or global extreme values of the previously recorded values of the second operating parameter, o determining, in a third step for removal of gas, those values (510) of the first operating parameter that are assigned to the previously determined extreme values of the second operating parameter, o operating the pump, in a fourth step for removal of gas, such that it assumes, for a predetermined period of time, one of the values of the first operating parameter that are assigned to the extreme values of the second operating parameter.