In an actuator unit for an injection system of an internal combustion engine, the difference in the longitudinal extension when a change of temperature of the piezoelectric actuator element occurs affecting the actuator unit is equalized compared to the actuator housing due to different thermal expansion coefficient values in that a fastening element is arranged on the actuator housing. The fastening element is made of a different material than the actuator housing and thus affects a force acting counter to the change of length of the actuator housing.