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The R package multgee implements the local odds ratios generalized estimating equations (GEE) approach proposed by Touloumis, Agresti, and Kateri (2013), a GEE approach for correlated multinomial responses that circumvents theoretical and practical limitations of the GEE method. A main strength of multgee is that it provides GEE routines for both ordinal (ordLORgee) and nominal (nomLORgee) responses, while relevant other softwares in R and SAS are restricted to ordinal responses under a marginal cumulative link model specification. In addition, multgee offers a marginal adjacent categories logit model for ordinal responses and a marginal baseline category logit model for nominal responses. Further, utility functions are available to ease the local odds ratios structure selection (intrinsic.pars) and to perform a Wald type goodness-of-fit test between two nested GEE models (waldts). We demonstrate the application of multgee through a clinical trial with clustered ordinal multinomial responses.