In a diagnostic system, messages which have occurred are collected and buffered with a short diagnostic test which is implemented in a control unit onboard the vehicle. The collected data are then transmitted into a memory area of the portable electronic driving authorization record, which therefore always contains the result of a short diagnostic test which has been carried out onboard. The result of this short diagnostic test is read out from the memory of the driving authorization record with a computer system in the customer reception of a servicing workshop, and is processed with a more wide-ranging diagnostic algorithm which builds on the result of the short diagnostic test.