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This paper describes a new concept for locomotion of miniature robots based on periodic electromagnetic actuation of magneto-sensitive elastomer bodies. The morphology of the robots relies on the dynamics of resonance for locomotion. Based on the described principle two prototypes are presented. The first prototype incorporates an inelastic polymeric frame with an integrated micro-coil and an attached magnetosensitive elastomeric body. The movement of the robot without moving parts exposed to the environment is bidirectional, the locomotion direction is frequency-controlled. The second prototype consists of only a symmetric magnetosensitive elastomeric body with 6 embedded micro-coils and is an example for compliant planar locomotion systems using the introduced actuating mechanism. The working principle of both prototypes is discussed with the help of transient dynamic analyses and verified with experimental tests.