Methods for T1 relaxation and diffusion measurements based on magnetic resonance signals from laser-hyperpolarized 129Xe nuclei are introduced. The methods involve optimum use of the perishable hyperpolarized magnetization of 129Xe. The necessary theoretical framework for the methods is developed, and then the methods are applied to measure the longitudinal relaxation constant, T1, and the self-diffusion constant, D, of hyperpolarized 129Xe. In a cell containing natural abundance 129Xe at 790 Torr, the T1 value was determined to be 155 +/- 5 min at 20 degrees C and at 2.0 T field. For a second cell at 896 Torr, at the same field and temperature, the T1 value was determined to be 66 +/- 2 min. At a higher field of 7.05 T, the T1 values for the two cells were found to be 185 +/- 10 and 88 +/- 5 min, respectively. The 129Xe self-diffusion constant for the first cell was measured to be 0.057 cm2/ s and for the second cell it was 0.044 cm2/s. The methods were applied to 129Xe in the gas phase, in vitro; however, they are, in principle, applicable for in vivo or ex vivo studies. The potential role of these methods in the development of newly emerging hyper-polarized 129Xe MRI applications is discussed.