Trifunctional poly‐ε‐caprolactone polyol was polymerized with a chain‐extended 1,6‐hexane diisocyanate, and the rheology followed by cone and plate flow. Viscosity was found to be independent of shear rate up to at least 102 N.s/m2 (103 poise) and 30s−1. Extent of reaction was monitored by a periodic titration for isocyanate groups. Using branching theory, viscosity was related to extent of reaction and temperature. Such relations should be useful for process models. Normal force data for the curing system are also reported.