Significant shifts of the frequency of the Raman spectra of the tangential mode of single walled carbon nanotubes (SWNTs) and fluorinated tubes (FSWNTs) in composites of polybutadiene (PB) were observed relative to the pristine SWNTs indicative of the interaction between the polymer and the SWNTs. Proton NMR line width measurements demonstrate partial suppression of polymer segmental motion for both types of nanotube composites and spin-lattice relaxation results indicate that short time-scale localized motions are also affected by SWNT inclusion, more so for FSWNTs. Hardness measurements as a function of wt% SWNTs and FSWNTs in the polymer show larger enhancements of hardness in the composite with the fluorinated tubes.