Many car-following models predict a stable car-following behavior with a very small fluctuation around an equilibrium value g∗ of the net headway g with zero speed-difference Δv between the following and the lead vehicle. However, it is well-known and additionally demonstrated by data in this paper, that the fluctuations are much larger than these models predict. Typically, the fluctuation in speed difference is around ±2 m/s, while the fluctuation in the net time headway T = g/v can be as big as one or even two seconds, which is as large as the mean time headway itself. By analyzing data from loop detectors as well as data from vehicle trajectories, evidence is provided that this randomness is not due to driver heterogeneity, but can be attributed to an internal stochasticity of the driver itself. A final model-based analysis supports the hypothesis, that the preferred headway of the driver is the parameter that is not kept constant but fluctuates strongly, thus causing the even macroscopically observable randomness in traffic flow.