A linear electric machine comprises a primary part (101) and a secondary part (102) linearly movable with respect to each other. The primary part comprises primary sections (103, 104) each having an airgap surface. The secondary part comprises secondary sections (105, 106) each having an airgap surface facing towards the air-gap surface of the respective primary section. Each primary section comprises force-generating windings (U1, V1, W1, U2, V2, W2) for generating a magnetic thrust force and a transversal magnetic force pulling the primary section towards the respective secondary section. The resultant of the transversal magnetic forces is controllable to levitate the primary part. The primary part further comprises one or more tilt-control windings (T1, T2) for controlling tilting of the primary part with respect to the secondary part.