Abstract: A turbomachine air starter, including a first compartment wherein non-overrunning elements of the air starter are situated, corresponding to elements which are only run in the turbomachine starting phase, and a second compartment wherein overrunning elements of the air starter are situated, corresponding to the elements which are run throughout an operating time of the turbomachine, including the starting phase. The first compartment includes an oil receptacle for oil splash lubrication of the non-overrunning elements, and the second compartment includes an AWC type oil cavity for lubrication of the overrunning elements supplied by the lubrication oil return of the overrunning elements, in turn supplied with pressurized lubrication oil supplied by the turbomachine, the receptacle and the cavity being internal to the air starter.