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The paper deals with bonus-malus systems with different claim types andvarying deductibles. The premium relativities are softened for thepolicyholders who are in the malus zone and these policyholders are subject toper claim deductibles depending on their levels in the bonus-malus scale andthe types of the reported claims. We introduce such bonus-malus systems andstudy their basic properties. In particular, we investigate when it is possibleto introduce varying deductibles, what restrictions we have and how we can dothis. Moreover, we deal with the special case where varying deductibles areapplied to the claims reported by policyholders occupying the highest level inthe bonus-malus scale and consider two allocation principles for thedeductibles. Finally, numerical illustrations are presented.

Bonus--malus systems with different claim types and varying deductibles