Clutch judder causes discomfort in a car. This undesirable event not only creates noise and vibrations, it also disturbs the normal functionality of other components in the driveline, especially the gearbox, which is prone to oscillating inputs. Although there are numerous separate studies on clutch judder and gearbox vibrations, a combined study is necessary in order to investigate the coupled dynamics, especially the effect of vibrations in a clutch on gearbox vibrations. In this paper, a dynamic model is presented for the driveline, including the details of a gearbox and a dry clutch. It allows us to investigate the effect of clutch parameters and to simulate conditions with and without judder. The obtained dynamical equations are then solved numerically. The influence of judder on gear dynamics and passenger comfort is investigated. The results show that judder causes loss of contact in the gearbox in most cases. In more severe cases of judder, it can cause rattle not only in the unloaded gear, but also in the loaded gears. A modal analysis and a frequency spectrum analysis are conducted as well in order to identify the frequency components of the system vibrations and to verify the obtained results. Parts of the results are compared with the theoretical and experimental data from other research studies, which show agreement and serve to validate the model in this work.