An MD80 was dispatched with an engine drive generator MEL'ed. At cruise the APU RPM oversped then began cycling down to 40% and back to normal dropping off line during the low cycle. An emergency was declared and the flight diverted to the nearest airport.

Narrative

Flight departed with an inoperative right engine driven generator (CSD disconnected -- MEL 24.16 engine driven generator inoperative) and properly deferred from prior inbound flight. After normal departure and climb to FL340; APU started to over speed (110%) and then wind down to 40% RPM while cycling the electrical power off line and forcing the only operating generator (left engine) to supply all electrical power. Descent to FL260 did not help the situation and the APU continued to wind up taking the electrical bus on line then winding down to 40% and dropping the bus off line. Emergency declared since down to one operating electrical generating source and made emergency landing at nearest suitable airport twenty miles away. Landing weight of 125;500 LBS put us well below maximum landing weight. The airfield rescue and fire fighting equipment was requested in the landing area in case of unknown failures. A normal landing and taxi in was made. These APU failures appear to be indicative of a previous company's MD-80's APU's; as they are weak; highly restrictive and are asked to work at their maximum far too often.