This paper discusses a new mechanism that may control the transition between stable sliding and cyclic stick-slip under variable normal stress condition. With a rate- and state-dependent friction law that embodies the effect of normal stress, a single degree of freedom spring-slider system inclined to the driving direction has a velocity-dependent critical stiffness which separates stable sliding and cyclic stick-slip. With steady state log-linear rate-dependent friction, the critical stiffness decreases with increasing velocity. Accordingly, higher velocity stabilizes a system for a predetermined stiffness lower than the critical value and may change the motion from cyclic stick-slip to stable sliding, and vice versa. Our numerical simulations in full dynamic motion confirmed such transition, and agreed well with the analytical calculation. Such transitions can also be found in experimental works. ¿ 1998 American Geophysical Union