Proton spin-lattice relaxation times,T₁, have been measured in the smectic phases, S_G², S_G¹ and S_A, and in the nematic phase of HxBPA, in the temperature range, 220K<T<360 K. In the S_G¹ and S_G² phases,T₁ has been measured at 15 and 40 MHz. The (S_G¹→S_G²) and (S_G²→S_G¹) transitions are clearly seen as discontinuities inT₁. The former transition is seen to be due to possible freezing or change of hydrocarbon chain motions of the molecule. Our data in the S_G¹ phase have been fitted to a model in which anisotropic rotational diffusion of the end hydrocarbon chains as also that of the rigid part of the molecule are considered. In the nematic phase, at 351 K, the observed behaviour ofT₁, measured in the frequency range, 5 to 40 MHz, agrees well with the theoretical predictions of Uklejaet al and Freed, who take into account long range collective order fluctuations and local reorientations. Using these theories, the correlation time for short range reorientations has been calculated from our results to be 4.3 × 10⁻¹⁰ and 1.1 × 10⁻⁹ s respectively.