Described is a series of INAA data reduction programs collectively known as TEABAGS (Trace Element Analysis By Automated Gamma-ray Spectrometry). The programs are written in FORTRAN and run on a Nuclear Data ND-6620 computer system, but should be adaptable to any medium-sized minicomputer. They are designed to monitor the status of all spectra obtained from samples and comparison standards irradiated together and to do all pending calculations without operator intervention. Major emphasis is placed on finding all peaks in the spectrum, properly identifying all nuclides present and all contributors to each peak, determining accurate estimates of the background continua under peaks, and producing realistic uncertainties on peak areas and final abundances.