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The singular characteristics of stress, electric displacement and magnetic induction fields near the tip of impermeable interracial cracks in two-dimensional magnetoelectroelastic bimaterials are studied using the generalized Stroh formalism. Two types of singularities are ob-tained: one is the oscillating singularity 1/2±iε, the other is the non-oscillating singularity 1/2±κ.It is found that the non-zero parameters e and κ cannot coexist for one transversely isotropic MEE bimaterial, a similar result is obtained for transversely isotropic piezoelectric bimaterials.