In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids by considering different electrical and magnetical crack-face boundary conditions is presented. For this purpose, a time-domain boundary element method (TDBEM) using dynamic fundamental solutions is developed. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is applied to compute the discrete boundary data and the generalized crack-opening-displacements. Iterative algorithms are implemented to deal with the non-linear electrical and magnetical semi-permeable crack-face boundary conditions.