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The dynamic mechanical and rheological properties of five long-chain branched (LCB) and three linear ethylene/propylene (EP) copolymers were investigated and compared using a dynamic mechanical analyzer (DMA) and an oscillatory rheometer. The novel series of LCB EP copolymers were synthesized with a constrained geometry catalyst (CGC), [C5Me4(SiMe2NtBu)]TiMe2, and had various propylene molar fractions of 0.01–0.11 and long-chain branch frequencies (LCBF) of 0.05–0.22. The linear EP copolymers were synthesized with an ansa-zirconocene catalyst, rac-Et(Ind)2ZrCl2 (EBI), and contained similar levels of propylene incorporation as the CGC copolymers, but no LCB. In dynamic mechanical analysis, the dynamic storage moduli (G′) and loss moduli (G″) of the copolymers decreased with an increase of propylene molar fraction. The α- and β-transitions of the CGC copolymers were overlaid with each other. High damping (tan δ) values were found with the CGC copolymers at temperatures below 0 °C. In oscillatory rheological analysis, compared to the linear EBI counterparts, the LCB CGC copolymer melts showed higher zero shear activation energies, broader plateaus of δ and larger elastic contributions, which are essential characteristics of LCB polymers. It was found that the long chain branching was the determining factor in controlling rheological properties of the polymer melts while the short chain branching from propylene incorporation played a decisive role in affecting dynamic mechanical properties. This work represents the first rheological evidence of LCB in EP copolymers synthesized with CGC.