Abstract
Two variations are proposed on a well-known car-following law, which treat the special case of return to uniform speed after a disturbance. According to the principles set forth, it appears (i) that oscillations with fixed or increasing amplitude practically never exist, (ii) decreasing oscillation can, however, arise if the uniform speed reached after the perturbation is below a certain value which increases with increase in the following driver's sluishness in perception and roughness in execution of driving manoeuvres.