The objective of this study was to determine the viscoelastic properties of natural (starch and protein) blends and synthetic biodegradable aliphatic copolyester blends. Blends of natural and synthetic biodegradable poly(butylene succinate) were cast into sheets using a coathanger die and then subjected to stress relaxation and creep tests at various temperatures. The natural content was varied at 10%, 30%, and 50% by weight. In some formulations a small (5% by weight) amount of compatibilizer was added. The materials were blended using a twin screw-extruder, pelletized, and sheeted using a coathanger die. The decay of stress upon the imposition of constant strain showed two regions, an exponential and power law; the stresses relaxed sharply at the initial stage and then decayed at a reduced rate for the duration of the experiment. The addition of compatibilizers increased the time required for the stress to relax compared to uncompatibilized blends of the same composition. Similarly, as the natural content increased the time taken to relax to a specified stress level decreased. Increased temperature enhanced the relaxation process. The initial strain of the creep curves was affected by the natural content; the higher the natural content, the lower the initial strain for the samples upon imposition of a constant stress. Similarly, the presence of compatibilizer in the blend reduced the initial strain for samples containing the same natural content. As the natural content of the blend decreases, the time required to attain the plateau compliance is reduced. The equilibrium compliance increased with temperature. These behaviors are described in terms of blend morphology. The empirical Struik and power law models can be used to fit the compliance data well.