With the increasing interest in fiber sensors based on polymer optical fibers, it becomes fundamental to determine the real applicability and reliability of this type of sensor. The viscoelastic nature of polymers gives rise to questions about the mechanical behavior of the fibers. In particular, concerns on the response in the nonstatic regime find foundation in the viscoelasticity theory. We investigate the effects of such behavior via analysis of the mechanical properties under dynamic excitations. It is shown that for low strain (0.28%), the Young's modulus is constant for frequencies up to the limit set by our measurement system. A more detailed analysis shows that viscoelastic effects are present and that they increase with both applied strain and frequency. However, the possibility of developing sensors that measure small dynamic deformations is not compromised. A stress-relaxation experiment for larger deformations (2.8%) is also reported and a relaxation time around 5 s is measured, defining a viscosity of 20 GPa·s.