The dynamics of regioregulated poly(4-methylthiazole-2,5-diyl) (HH-P4MeTz) was investigated by solid-state $^{1}\mathrm{H},\phantom{\rule{0.3em}{0ex}}^{2}\mathrm{D}$, and $^{13}\mathrm{C}$ NMR spectroscopies, and differential scanning calorimetry (DSC) measurements. DSC, $^{2}\mathrm{D}$ quadrupolar echo NMR, $^{13}\mathrm{C}$ cross-polarization and magic-angle spinning (CPMAS) NMR, and two-dimensional spin-echo CPMAS NMR spectroscopy suggest existence of a quasiordered phase in which backbone twists take place with weakened $\ensuremath{\pi}$ stackings. Two-dimensional exchange $^{2}\mathrm{D}$ NMR (2DEX) detected slow dynamics with a rate of an order of ${10}^{2}\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ for the $\mathrm{C}{D}_{3}$ group in ${d}_{3}$-HH-P4MeTz at 288 K. The frequency dependence of proton longitudinal relaxation rate at 288 K shows a ${\ensuremath{\omega}}^{\ensuremath{-}1∕2}$ dependence, which is due to the one-dimensional diffusionlike motion of backbone conformational modulation waves. The diffusion rate was estimated as $3\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$, which was approximately ${10}^{7}$ times larger than that estimated by 2DEX NMR measurements. These results suggest that there exists anomalous dispersion of modulation waves in HH-P4MeTz. The one-dimensional group velocity of the wave packet is responsible for the behavior of proton longitudinal relaxation time. On the other hand, the 2DEX NMR is sensitive to the phase velocity of the nutation of methyl groups that is associated with backbone twists. From proton ${T}_{1}$ and ${T}_{2}$ measurements, the activation energy was estimated as 2.9 and $3.4\phantom{\rule{0.3em}{0ex}}\mathrm{kcal}∕\mathrm{mol}$, respectively. These were in agreement with $3.0\phantom{\rule{0.3em}{0ex}}\mathrm{kcal}∕\mathrm{mol}$ determined by a M\o{}ller-Plesset molecular orbital calculation. We also performed a chemical shielding calculation of the methyl carbon in order to understand chemical shift tensor behavior, leading to the fact that a quasiordered phase coexists with the crystalline phase.