Various semifluorinated polymers of narrow molar mass distributions and definitely changed molecular structure are employed as model substances to investigate the impact of the polymer architecture on key rheological properties in the linear range of shear flow. These model samples originate from free radical terpolymerizations of tetrafluoroethylene (TFE), hexafluoropropylene (HFP), and vinylidenfluoride (VDF), referred to as THV. They were tailored to cover a broad range of mass-average molar masses of a straight linear and of a long-chain branched topography. By the controlled incorporation of long-chain branches (LCB) into the fluoropolymers, a complex thermorheological behavior is observed. The effect of long-chain branching also becomes evident by dynamic-mechanical measurements represented by a plot of the angle delta versus the complex modulus \G*(omega)\. Compared to the linear reference materials for which eta(0) similar to M-w(3.8) was found, the zero-shear rate viscosity eta(0) of some of the branched polymers is significantly higher than that of a linear product with equivalent M-w, for others it comes to lie below the curve for linear samples. The experimental eta(0) (M-w) data of the branched THV are in good agreement with an approach proposed by Janzen and Colby using the structural information from the molecular characterization. Moreover, it was found that plotting eta(0) as a function of the intrinsic viscosity [eta] more sensitively discriminates between the various long-chain branched samples than eta(0) (M-w). Comparing the sensitivity of methods based on rheological properties in solution and in the molten state, it is demonstrated that the linear behavior of the melts can very favorably be used to get an insight into the molecular architecture of THV polymers.