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We present a new family of high order accurate Arbitrary-Lagrangian-Eulerian(ALE)one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions.We consider the 3D Euler equations of compressible gas dynamics,the equations of classical ideal magnetohydrodynamics(MHD)as well as the non-conservative seven-equation Baer-Nunziato model with stiff relaxation source terms.