Solutions are developed for Burgers' equation and for the surface water content subject to one-dimensional drainage. These are found as limiting cases of Richards' equation using diffusivity and conductivity functions from Fujita as extended by Broadbridge and White. The solution from Burgers' equation can generally be expressed as a function of only a dimensionless time, depth, and initial reduced water content. For the more strongly nonlinear case, initially the surface water content decreases in proportion to the square root of time. For large times, the surface water content approaches the residual water content inversely with the square root of time. ¿ American Geophysical Union 1995