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