The invention relates to a dry-compressing dual-shaft rotary displacement screw spindle pump machine for delivering and compressing gases. The spindle rotor pair therein includes multiple stages, having a primary delivery thread, a secondary delivery thread and a gas outlet collector chamber therebetween. The primary delivery thread head circle diameter decreases in the gas outlet direction, while the foot circle diameter thereof increases correspondingly for an application-specific matching inner “integral” compression ratio. The secondary delivery thread nominal delivery direction is opposite to the primary delivery thread nominal delivery direction. The secondary delivery thread is implemented such that the actual gas flow direction is opposite to the nominal delivery direction thereof, and is always directed away from the gas outlet plenum, having a gas permeation under ambient pressure just as the space in the gearbox. A control gas delivery stage is additionally provided for very high operating pressures.