Constant flux infiltration experiments were performed at rates less than saturated hydraulic conductivity (Ksat) on uniform columns of soils and glass beads with low initial water contents. Tensiometers measured matric pressure (&psgr;) histories at various depths in the 0.05-m diameter, 0.73-m-tall columns. One of two devices applied the steady fluxes: one was a ceramic plate applicator that allowed monitoring of pressures above the plate, and the other was a rain applicator that sprinkled water uniformly over the surface. Two columns were used. One allowed destructive sampling for water content in a way that prevented postrun changes in water content. The other allowed prerun replacement of pore air with gases of different solubilities. Contrary to predictions based on the Richards equation, transmission zone &psgr; values passed through maxima, then decreased continuously as wetting fronts moved down columns. Such nonideal behavior was observed in Aiken silt loam, Hanford sandy loam, Delhi sand, Oakley sand, and glass beads. At an infiltration rate equal to 70% of Ksat, values of &psgr; at 2, 5, and 8 cm depths in the glass beads column decreased an average of 52% from their respective maxima in about 3 hours. In the soil columns the nonmonotonic behavior was less pronounced but statistically significant at all rates examined (3--59% of Ksat). Matric pressure reversals were larger, and corresponding maxima higher, when a given rate was preceded by a series of stepwise increasing rates. Tests of possible explanations provided no evidence to support hypotheses involving trapped-air dynamics, convective air flow, particle rearrangement, or experimental artifacts. The results cast doubt on the ability of the Richards equation to predict the course of constant flux infiltration including the initiation of runoff. ¿ American Geophysical Union 1993