Methods are presented for estimating peak-flow magnitudes of selected frequencies for drainage basins in Delaware. The methods were developed by generalized least-squares regression techniques using data from 74 streamflow-gaging stations in and near Delaware, and apply to peak flows with recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years. The State is divided into two hydrologic regions--the Piedmont region, and the Coastal Plain region. Sets of equations for calculating peak discharges based on physical basin characteristics and their associated standard errors of prediction are provided for each hydrologic region. Basin characteristics and flood-frequency characteristics are tabulated for 74 streamflow-gaging stations in Delaware and surrounding States. Methods of estimating peak flows at sites in Delaware for ungaged and gaged locations are presented.