Equations for estimating flood discharges for exceedance probabilities of 0.50, 0.20, 0.10, 0.04, 0.02, and 0.01 at ungaged sites in New Mexico were developed and updated from streamflow gaging station data through 1982. The 1984 data from selected stations in the southwestern part of the State were also used because of the high discharges that occurred. The State was divided into eight physiographic regions and equations were developed for each region. The logarithms of annual flood peaks for the respective exceedance probabilities were related to logarithms of basin and climatic characteristics. The average standard error of estimate of a flood peak for an exceedance probability of 0.01 ranged from 44% to 81%, a significant improvement over previous studies. New techniques for weighting independent estimates of flood discharges at gaging stations by each estimate 's variance are presented. The variances are the squares of the standard errors. Standard errors of the estimated flood discharges for the exceedance probabilities are presented for all streamflow gaging stations. Flood frequency characteristics at 219 gaging stations are also included. (Author 's abstract)