The Theology of supramolecular polycaprolactone polymers with two ureidopyrimidinone (UPy) end groups and unimer molecular weights between 600 and 4000 was compared with that of branched tri- and tetrafunctional analogs. Above the melting point of polycaprolactone, the previously observed(1) low-frequency plateau in storage and loss moduli during oscillatory frequency sweep of lower molecular weight bifunctional unimers was shown to persist up to 130-170 degrees C, where it gradually disappeared but reappeared upon slow cooling. Even though they are supramolecularly cross-linked, the tri- and tetrafunctional materials showed no plateau. This counterintuitive behavior was further investigated with optical microscopy, WAX S, and DSC experiments, which indicated that the plateau is closely connected to the presence of crystalline domains in the lower molecular weight fraction of bifunctionalized unimers. Because the formation of crystallites is prevented by branching, and because the network formed by the tri- and tetrafunctional unimers has a short lifetime, the branched materials do not show a low-frequency plateau.