A parameter estimation procedure, sequential uncertainty domain parameter fitting (SUFI), is presented and has the following characteristics. The procedure is sequential in nature, meaning that one more iteration can always be made before choosing the final estimates. The procedure has a Bayesian framework, indicating that the method operates within uncertainty domains (prior, posterior) associated with each parameter. The procedure is a fitting procedure, conditioning the unknown parameter estimates on an array of observed values. Finally, the procedure is iterative, requiring a stopping rule which is provided by a critical value of a goal function. Performance of the SUFI parameter estimation procedure is demonstrated using three examples of increasing complexity: (1) analysis of a solute breakthrough curve measured in the laboratory during steady state water flow, (2) estimation of the unsaturated soil hydraulic parameters from a transient drainage experiment carried out in a 6-m deep lysimeter, and (3) estimation of selected flow and transport parameters from a hypothetical ring infiltrometer experiment. The procedure was found to be general, stable, and always convergent.¿ 1997 American Geophysical Union