  The paper concerns about the uniform decaying property (abbreviated by UDP)
of solutions for an anisotropic viscoelastic system in the form of
integrodifferential system (abbreviated by VID system) with mixed type boundary
condition. The mixed type condition consists of the homogeneous displacement
boundary condition and a homogeneous traction boundary condition or with a
dissipation. By using a dissipative structure of this system, we will prove the
UDP in a unified way for the two cases, which are, when the time derivative of
relaxation tensor decays with polynomial order and it decays with exponential
order.
