- We study the presence of chaos in a car-following traffic model based on a system of delay-differential equations. We find that for low and high values of cars density the system has a stable steady-state solution. Our results show that above a certain time delay and for intermediate density values the system passes to chaos following the Ruelle-Takens-Newhouse scenario (fixed point–limit cycles–two-tori–three-tori–chaos). Exponential decay of the power spectrum and non-integer correlation dimension suggest the existence of chaos. We find that the chaotic attractors are multifractal.