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Rmfit uses a forward-folding technique to obtain the best-fit parameters for a chosen model given user-selected source and background time intervals from data files containing observed count rates and a corresponding detector response matrix. rmfit displays lightcurves and spectra using a graphical interface that enables user-defined integrated or time-resolved spectral fits and binning in either time or energy. Originally developed for the analysis of BATSE Gamma-Ray Burst (GRB) spectroscopy, rmfit is a tool for the spectroscopy of transient sources; it accommodates the Fermi GBM and LAT data and Swift BAT.