An electromechanical displacement device (81) provided with a holder (90), an element (45) displaceable relative to the holder (90), and an actuator (83) connected to the holder (90) by which the element (45) can be displaced relative to the holder (90). The actuator (83) is provided with at least a first and a second clamping member (B, A) which can be clamped alternately against the element (45) under a mechanical pretensioning force F.sub.k, at least one clamping member (A) being provided with at least one piezoelectric, electrostrictive or magnetostrictive clamping element (61). The actuator (83) is further provided with a piezoelectric, electrostrictive or magnetostrictive transport element (69', 69") by which the distance between the clamping members (A, B) can be changed. When the first clamping member (B) is clamped against the element (45) under the mechanical pretensioning force F.sub.k while the second clamping member (A) is disengaged therefrom, activation of the clamping element (61) transfers the mechanical pretensioning force F.sub.k to the second clamping member (A), so that the second clamping member (A) is clamped against the element (45) under the mechanical pretensioning force F.sub.k, while the first clamping member (B) is disengaged therefrom.