Hyperpolarized (HP) ¹²⁹Xe yields high signal intensities in nuclear magnetic resonance (NMR) and, through its large chemical shift range of ∼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 ¹²⁹Xe over an extended time period. To this end, we have used commercially available gas exchange modules to continuously infuse concentrated HP ¹²⁹Xe 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 ¹²⁹Xe into the bloodstream in vivo. Additionally, we have developed a detailed mathematical model of the infused HP ¹²⁹Xe signal dynamics that should be useful in designing improved infusion systems that yield even higher dissolved HP ¹²⁹Xe signal intensities.