Methods have been developed for estimating magni- tude and frequency of floods at gaged and ungaged sites on streams in the southwestern United States. Estimating equations for ungaged sites that apply to small drainage basins were developed by transferring information from ungaged sites using techniques such as multiple regression and a hybrid method developed during this study. Drainage area, mean basin elevation, mean annual precipitation, mean annual evaporation, latitude, and longitude are the basin and climatic charac- teristics needed to use the equations. Flood- frequency relations and selected basin and climatic characteristics, updated through 1986 water year, are tabulated for more than 1,300 gaging stations in the southwestern United States. The study area was divided into 16 flood regions. Generalized least-squares regression was used to define the regression models in 12 regions with a sufficient number of defined flood-frequency relations at gaged sites. Four regions had more than 30 percent of the gaged sites with no defined relations, thus the regression method was not used because of the large amount of missing infor- mation. The hybrid analysis was used in those 4 regions, because it does not require individual flood-frequency relations and thus can use data for all gaging stations in a region. Average standard error of prediction for the 12 regions with generalized least-squares models ranged from 39 to 95 percent for the 100-year peak discharge. The estimated average standard error of the four hybrid models ranged from 0.44 to 1.8 log units for the 100-year peak discharge.