In this paper, we analysed theoretically the hunting stability of a high speed railway vehicle which has at least seven degrees of freedom with respect to lateral motion when elastic and frictional forces are connected in series against truck turning. According to the theoretical results, it was found that the stability criteria of the hunting, so-called, lower-center rolling, upper-center rolling and yawing of a car body, and the front and rear trucks depended on the lower hunting velocity was an unstable limit cycle, while the upper limit cycle changed into either a stable limit cycle or an unstable one corresponding to the magnitude of the angular amplitude. As the amplitude increased, the unstable region between the lower and upper limit cycles increased larger. Further, as the angular amplitude increased, the truck hunting phenomena of a bogie car connected with the damping of a suspension device between the car body and the trucks, the magnitude of the angular amplitude between the front and rear trucks, phase angle and others are made clear.