An air pump comprising a piston located inside a piston housing having a crown and an open end. The piston is provided with a pressure generating member in the form of a resilient membrane-like annular disc which is held centrally on one end of the piston, which is fitted in the piston housing with the annular disc and the piston plate pointed towards the crown of the piston housing whereby the rim of the membrane-like annular disc bears against the inner wall of the piston housing and the piston housing is guided on the piston in a manner enabling it to be moved axially.