This article constructs statistical models for clustered ordinal measurements. We specify two regression models: one for the marginal means and one for the marginal pairwise global odds ratios. Of particular interest are problems in which the odds ratio regression is a focus. Simple assumptions about higher-order conditional moments give a quadratic exponential likelihood function with second-order estimating equations (GEE2) as score equations. But computational difficulty can arise for large clusters when both the mean response and the association between measures is of interest. First, we present GEE1 as an alternative estimation strategy. Second, we extend to repeated ordinal measurements the method developed by Carey et al. for binary observations that is based on alternating logistic regressions (ALR) for the marginal mean parameters and the pairwise log-odds ratio parameters. We study the efficiency of GEE1 and ALR relative to full maximum likelihood. We demonstrate the utility of our regression methods for ordinal data by applying the methods to a surgical follow-up study.