A compressor or pump, including at least one compressor or pump element for pressurised supply of a fluid to a network of consumers of such pressurised fluid; a motor coupled with the compressor or pump element. The compressor or pump is equipped with a control having a basic control for the nominal regulation of one or more control parameters (Q, pw) as a function of a desired, set working point of the compressor within the nominal set working range of the compressor or pump, set during design. The control is further provided with an additional control function for static or dynamic adjustment of the working range limit values. The nominal control range of one or more control parameters is adjusted as a function of the actual working conditions of the compressor or pump that deviate from the nominal working conditions.