The spin-lattice relaxation time and temperature-dependent chemical shift of Xe131 in liquid and solid xenon have been measured between 9 and 250°K. A calculation of the transition probabilities for quadrupolar relaxation of Xe131 in solid xenon via the Raman process is described. The calculation is based on the theory of Van Kranendonk, modified for the case of a face-centered cubic lattice with electric-field gradients arising from exchange and van der Waals interactions. The data are shown to verify the predicted temperature dependence of T1 in the solid above 9°K and the absolute magnitude of T1 at 100°K. It is demonstrated that the temperature dependence of the data is consistent with the temperature variation of the Debye temperature Θ obtained by Packard and Swenson from specific-heat measurements. Quadrupolar relaxation via diffusing impurities was observed at temperatures near the melting point in solid xenon samples containing roughly 1% air. The quadrupolar relaxation time of Xe131 in liquid xenon was found to vary exponentially with temperature with an "activation energy" EA=640+/-30 cal/mole. This "activation energy" is approximately one-half as large as values previously obtained for the activation energy of self-diffusion in liquid xenon. Measurements of the chemical shift of Xe131 indicate that the local field increases linearly with density in liquid and solid xenon. Least-squares fits to the data yield the change ∆H of the external resonant field with density: - (1H0)[∂(∆H)∂ρ]=(5.1+/-0.5)×10- 7 (amagat)-1 in liquid xenon and - (1H0)[∂(∆H)∂ρ]=(18.2+/-1.1)×10- 7 (amagat)-1 in solid xenon. These data support the previous Xe129 shift data of Yen and Norberg but disagree with more recent measurements by Brinkmann and Carr of the density dependence of the Xe129 shift in solid xenon.