Kinetically controlled volatilization and dissolution of nonaqueous phase liquids (NAPLs) may play an important role in the transport of volatile compounds in the unsaturated (vadose) zone. In this study, some one- and two-dimensional steady state transport problems are solved analytically. The one-dimensional case is pertinent to pollution by a relatively long, mainly horizontally spread leak of NAPL. The two-dimensional case corresponds to situations in which the pollution spreads primarily vertically, originating at the ground surface and migrating to the top of the capillary fringe, and in which the solution domain may be represented by a cross-sectional model. Solutions of the steady state transport problems are used to investigate effects of several parameters, characterizing the advective-dispersive and purely diffusive transport regimes, on the NAPL concentration distribution for the one- and two-dimensional cases, respectively. Results of this analysis indicate that the mass exchange between NAPL and other phases may not reach equilibrium, even for relatively large mass transfer rate coefficients and small water infiltration rates, if this zone has relatively small vertical or horizontal extent and is located close to the fully open ground surface. Analysis of local volatilization and dissolution fluxes shows that, under equilibrium conditions, the main losses of the organic phase take place at the upper part of the NAPL zone. ¿ American Geophysical Union 1993