Three different fluoro-terminated hyperbranched poly(ether ketone)s (FHBPEKs) with variable degrees of branching and their linear analogous poly(ether ketone) (LPEK) whose chemical Structure and molecular weight were similar to those of the FHBPEKs were synthesized. Cyano-terminated hyperbranched poly(ether ketone), CHBPEK, in which the terminal groups of FHBPEK were modified with cyanophenol was also prepared as a reference. The local relaxation and motion of the three FHBPEKs, in conjunction with their hyperbranched structure and the degrees of branching, were characterized by the solid-state H-1 pulsed wide-line NMR spectroscopy and compared to that of the linear counterpart, LPEK. From the measurements of the spin-lattice relaxation times in the rotating frame, T-1 rho's, over the temperature range 140-400 K, the correlation times, tau(c)'s, and the corresponding activation energies, E-a's, were determined, providing a direct evaluation for the local molecular motion. FHBPEKs were found to be structurally heterogeneous because they had two different motions throughout the system; with aid of the tau(c) results of CHBPEK, each was assigned as originating from the linear and from the terminal/branched portion, respectively. In contrast, LPEK exhibited single relaxational and motional behavior, indicating that it was structurally homogeneous. The molecular mobility of the linear portion of FHBPEKs was higher than that of LPEK and enhanced with increasing degree of branching in the entire range of experimental temperatures. For the terminal/branched portion of the FHBPEKs, the local mobility was little affected by the degree of branching, especially at the temperature range from 140 K to room temperature, but increased afterward as was for the linear portion.