The negative binomial (NB) is a member of the exponential family of discrete probability distributions. The nature of the distribution is itself well understood, but its contribution to regression modeling, in particular as a generalized linear model (GLM), has not been appreciated. The mathematical properties of the negative binomial are derived and GLM algorithms are developed for both the canonical and log form. Geometric regression is seen as an instance of the NB. The log forms of both may be effectively used to model types of POisson-overdispersed count data. A GLM-type algorithm is created for a general log-negative binomial regression (LNB) which iteratively estimates a heterogeniety factor in addition to parameters and standard errors. Applications in terms of data generated from a NB random number generator are presented and modeled using a LNB SAS macro and a like program written in Stata. (c) 1992, 1993 (revised) Joseph Hilbe [Note: Manuscript prepared September, 1992; SAS macro added December 1993, with a macro revision in 1994]