When a soft tube is inflated, it may sometimes show a bulge instability wherein a portion of the tube inflates much more than the rest. The bulge instability is well-understood for hyperelastic materials. We examine inflation of polyurethane tubes whose material behavior is not strictly hyperelastic. Upon inflating at constant rate, the tubes deform into a variety of shapes including irregular axisymmetric shapes with multiple localized bulges, a single axially-propagating bulge, or homogeneous cylindrical shapes. In all cases regardless of the inflation mode, the pressure first rises to a maximum, and then gradually reduces towards a plateau. We document numerous differences as compared to hyperelastic tubes. Most notably a pressure maximum can appear even without bulging, whereas for hyperelastic tubes, a pressure maximum is necessarily accompanied by bulging. Further, the decrease in pressure beyond the maximum occurs gradually over timescales as long as an hour, whereas bulging of hyperelastic tubes induces an instantaneous drop in pressure. We also observe permanent deformation upon deflation, a decrease in the pressure maximum during a subsequent second inflation, and more severe bulge localization at low inflation rates. Existing theory of hyperelastic tube inflation cannot capture the observed behaviors, even qualitatively. Finite element simulations suggest that many of the observations can be explained by viscoelasticity, specifically that a slow material response allows the pressure to remain high for long durations, which in turn allows growth of multiple bulges.