Hyperpolarized (HP) Xe-129 yields high signal intensities in nuclear magnetic resonance (NMR) and, through its large chemical shift range of similar to 300 ppm, provides detailed information about the local chemical environment. To exploit these properties in aqueous solutions and living tissues requires the development of methods for efficiently dissolving HP Xe-129 over an extended time period. To this end, we have used commercially available gas exchange modules to continuously infuse concentrated HP Xe-129 into flowing liquids, including rat whole blood, for periods as long as one hour and have demonstrated the feasibility of dissolved-phase MR imaging with submillimeter resolution within minutes. These modules, which exchange gases using hydrophobic microporous polymer membranes, are compatible with a variety of liquids and are Suitable for infusing HP Xe-129 into the bloodstream in vivo. Additionally, we have developed a detailed mathematical model of the infused HP Xe-129 signal dynamics that should be useful in designing improved infusion systems that yield even higher dissolved HP Xe-129 signal intensities.