Advanced driver assistance systems such as adaptive cruise control (ACC) and lane keeping system (LKS) potentially contribute to reducing crash rates and traffic congestion. On-road studies based on early ACC systems operational at medium–high speeds only have shown that the system reduces the proportion of short time gaps when activated. Despite the effects on driver behaviour, most mathematical models assessing the impact of ACC and LKS systems on crash rates and traffic congestion are not based on empirical findings. This study examines the factors that influence changes in the longitudinal vehicle control when driving with ACC and LKS. The data were collected in a naturalistic driving experiment with full-range ACC and LKS and two different vehicle brands (BMW and Tesla) in the Netherlands. To capture changes that are relevant for traffic safety, speeding and a time gap shorter than one second were investigated. The factors influencing speeding and short time gaps were analysed using statistical tests and logistic regression models with random effects, that allow to control for the impact of different explanatory variables and correlations between repeated 10-s intervals over time. The findings revealed that, overall, drivers were less likely to speed and they were also less likely to have a time gap shorter than one second in the experimental condition with the ACC and the LKS than in the baseline condition in manual driving. Drivers were likely to speed in the following 10-s interval when the current speed was close to the speed limit, and/or when the next speed limit was lower than the current speed limit, and/or when the acceleration was high. Drivers were likely to have a short time gap in the following 10-s interval when approaching a slower leader, and/or when the current time gap was short and/or when the acceleration was high. Controlled for these main factors, drivers were less likely to speed and to have a short time gap when the ACC and the LKS were active. However, drivers were more likely to speed when overruling the ACC by pressing the gas pedal. When the systems were active, one vehicle brand showed a smaller probability of a short time gap than the other brand, suggesting differences in ACC system settings between brands. In addition, the speeding probability increased while the probability of a short time gap decreased over time during the trip after the activation of the systems. Although further studies including a larger sample of participants and a wider range of traffic situations are needed, the results are useful to the design of automated vehicles that prevent speeding and short time gaps, and to the implementation of traffic simulations that evaluate the impact of ACC and LKS on crash rates and traffic congestion according to realistic on-road data.