In recent years, NMR with hyperpolarized (HP) xenon inside functionalized host structure (e.g., cryptophanes) have become a potential candidate for the direct observation of metabolic processes (i.e., molecular imaging). A critical issue for real applications is the dissolution of the HP-gas in the liquid which contains the host. In this work, we present recent developments for an improved and controlled dissolution of HP-Xe in liquids using hollow fiber membranes and different compressor systems. The designed apparatus consists of a compressor and a membrane unit. The compressor provides HP-Xe-129 continuously at small adjustable pressures and in a polarization-preserving way. The membrane unit enables a molecular solution of the HP-gas in aqueous liquids, avoiding the formation of bubbles or even foams. Two different types of compressors were tested in terms of function and useful materials. Special emphasis was put on a systematic reduction of transfer losses in the gas and liquid phase. In order to optimize the system parameters, several physical models were developed to describe the transport and the losses of nuclear polarization. Finally, the successful implementation was demonstrated in several experiments. HP-Xe was dissolved in an aqueous cryptophane-A-(OCH2COOH)(6) solution, and stable Xe signals could be measured over 35 min, only limited by the size of the gas reservoir. Such long and stable experimental conditions enabled the study of chemical exchange of xenon between cryptophane and water environments even for a time-consuming 2D NMR experiment. The good signal stability over the measurement time allowed an exact determination of the residence time of the Xe atom inside the cryptophane, resulting in an average residence time of 44.5 +/- 2.7 ms.