The class of aircraft known as gyroplanes (orautogyros) helped to pave the way for thedevelopment of the helicopter. However, they havefound no application in contemporary commercial ormilitary aviation. It is in recreational or sportflying that the gyroplane has proved popular. Mostif not all designs are however homebuilts, and as aconsequence little analysis of any significance hasbeen conducted on the flight mechanics of theseaircraft. This Paper presents an analysis of thelongitudinal stability of gyroplanes. Simpleconsideration of the basic forces and moments thatmight influence stability, in the context ofelementary rotor behaviour, is used to assess thefundamental nature of gyroplane longitudinalstability. This is quantified by the application ofa sophisticated generic rotorcraft mathematicalmodel to the gyroplane problem. It is concluded thatthe basic configuration can be longitudinally stablewith appropriate design, and that the rotorspeeddegree of freedom must also be included whenmodelling the aircraft.