In this paper, the dynamic interactions among cracks embedded in a two-dimensional (2-D)piezoelectric-piezomagnetic composite material are analyzed by means of a hypersingular formulation of the boundary element method. In the numerical solution procedure, extended crack opening displacements and extended traction jumps across the crack are considered as basic unknowns, so that only the traction boundary integral equations are needed on the crack surfaces. Quadratic discontinuous boundary elements are implemented together with discontinuous quarterpoint elements placed next to the crack tips to ensure a proper representation of the square root asymptotic behavior. Several impermeable cracks configurations subjected to time-harmonic incident L-waves are analyzed in order to characterize the effects of the magnetoelectromechanical coupling on the dynamic crack interactions and to illustrate the dependence on such coupling of the fracture parameters: stress intensity factors, electric displacement intensity factor and magnetic induction intensity factor.