We can assume that hyperelasticity is a good constitutive model for the rubber behavior. But there is not perfect hyperelastic rubber and, in some regime, viscoelastic effects should be observed (hyperelasticity is a model, not a real object). The key point in these kind of materials is the time scale: if the time scale is short, the material is more elastic, and if the time scale is long, the material is more viscous. So probably, for fast processes you can model the rubber as an hyperelastic model, and for low processes as a viscoelastic  one.

Check next link: https://www.youtube.com/watch?v=Q1VtAXeMn74