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The existence of shear horizontal surface waves in a magneto-electro-elastic (MEE) half-space with hexagonal (6mm) symmetry is investigated.The surface of the MEE half-space is mechanically free, but subjected to four types of electromagnetic boundary conditions.These boundary conditions are electrically open/magnetically closed, electrically open/magnetically open, electrically closed/magnetically open and electrically closed/magnetically closed.It is shown that except for the electrically open/magnetically closed condition, the three other sets of electromagnetic boundary conditions allow the propagation of shear horizontal surface waves.