My work looks at the bounds on the quasistatic response of viscoelastic two-phase composites when subject to time-varying applied fields. When at least one of the two two constituent materials in the composite has viscoelastic behavior with a continuous spectrum of relaxation times, it is expected that the composite will have similar behavior. The exact response of the composite, however, depends also on the composite’s geometry. By performing an optimization process over all possible microstructures, we can determine the maximum and minimum values of the response of the composite at a specific moment in time. The goal is to first apply this technique to composites where one constituent is a viscoelastic material while the other is a void and then extend the method to composites with three constituents in which two are viscoelastic and the remainder is a void, such as the composite materials used in 3D printing.