This study of the effect of excess rainfall, ponded without runoff, on the dynamics of infiltration into a deep homogeneous soil uses the Green--Ampt, or delta function, approximation. Exact solutions are given for constant and for piecewise constant rainfall. An inverse method yields solutions for arbitrary hyetographs. Ponding can increase markedly both the total duration of the infiltration event and the total amount infiltrated. The analysis suggests that capillary hysteresis emerges during the ponding recession phase toward the end of a storm. In long-duration heavy rainstorms infiltration rate may increase with time, contrary to the classical picture. The asymptotic large time infiltration rate under continuous constant rainfall at rate R, with R≥K¿ (the conductivity parameter in the Green--Ampt formulation) is an increasing function of both K¿ and R. (With ponding neglected, it is simply K¿). An appendix gives some exact results on the influence of hyetograph shape on time to ponding. ¿ American Geophysical Union 1993