Predictions were made of the long-term behavior of a new repair system for gas pipelines, which involves the wrapping of a polymer composite tape coated with a pressure-sensitive adhesive on the damaged pipe. The time- and temperature-dependent behavior of the tape and the adhesive was experimentally evaluated using constant strain rate tests. A theoretical model was developed for the winding, taking into account the nonisothermal viscoelastic behavior of the materials. A good agreement was found between theoretical predictions and full-scale experimental results.