A new method for flood-frequency analysis is developed using the concept of mixed distributions. A mixture of only two component distributions is shown to fit the various observed flood distributions. The two-distribution method is tested using annual flood series from 33 streams in Illinois. The flood distributions computed by this method fit the observed flood distributions better than other methods in use, insofar as the mean of absolute deviations of the computed floods from those observed is the least. The proposed method satisfactorily matches the medium and high floods which are of great interest to the engineers and hydrologists. An objective methodology has been formulated for computer application. The methodology is free from errors and uncertainties that exist when third and higher order moments are used for obtaining estimates of the component distribution parameters.