The article deals with the credibility regression models. The theory of credibility is a summary of methods used for a calculation and a systematic correction of the net premiums. The credibility models are designed for situations where the average claim amount evolves in time or depends on the other measurable factors. The methods of the regression analysis were for the first time used in the theory of credibility by Hachemeister. His model (model HM) was adjusted by De Vylder for the purpose of the practical application. Even though the Hachemeister's model does not result in a compromise premium, which is the basic requirement expected from the credibility models, it provided important information for De Vylder's model created in 1985. The main aim of this article is to show the alternatives of an application of DV85 model in the accident automobile insurance, i.e. in the mandatory contractual insurance.