The response time distributions of the frames sent on a Controller Area Network (CAN) bus are of prime interest to dimension and validate automotive electronic architectures. However, the existing work on the timing behaviour of the CAN network does not take into account that all the data exchanges between the Electronic Control Units (ECUs) are driven by different and independent clocks which are subject to clock drifts. This paper proposes a model for clock drifts and describes their impact on the CAN frame response time distributions. By implementing the clock drifts in a CAN simulation tool, we show experimentally that the response time distributions converge, for drift values chosen randomly within the same range on all ECUs, whatever the initial phasings between the sending nodes. Furthermore, we show that, as a result of the clock drifts, the situations leading to the worst case response times are transient.