To improve understanding of hysteretic air permeability relations, a need exists for data on the water content dependence of air permeability, matric pressure, and air trapping (especially for wetting-drying cycles). To obtain these data, a special instrument was designed. The instrument is a combination of a gas permeameter (for air permeability determination), a suction plate apparatus (for retentivity curve determination), and an air pycnometer (for trapped-air-volume determination). This design allowed values of air permeability, matric pressure, and air trapping to be codetermined, i.e., determined at the same values of water content using the same sample and the same inflow-outflow boundaries. Such data were obtained for two nonswelling soils. The validity of the air permeability determinations was repeatedly confirmed by rigorous tests of Darcy's law. During initial drying from complete water saturation, supplementary measurements were made to assess the magnitude of gas slip. The extended Darcy equation accurately described the measured flux gradient relations for each condition of absolute gas pressure tested. Air permeability functions exhibited zero-permeability regions at high water contents as well as an abruptly appearing hysteresis at low water contents. Measurements in the zero-permeability regions revealed that the total amount of air in general exceeded the amount of trapped air. This indicates that the medium' s air space is partitioned into three measurable domains: through-flowing air, locally accessible air (i.e., air accessible from only one flow boundary), and trapped air. During repeated wetting and drying, the disappearance and reappearance of air permeability coincided closely with the reappearance and disappearance, respectively, of trapped air. The observed relation between critical features of the air permeability functions and those of the air-trapping functions suggest that water-based blockages play a significant role in the disruption of gas-phase connectivity and in preventing air flow, and must be considered in any effectual model of air permeability relations.