We present a class of multivariate regression models for ordinal response variables in which the coeecients of the explanatory variables are allowed to vary as smooth functions of other variables. In the rst part of the paper we consider a semiparametric cumulative regression model for a single ordinal outcome variable. A penalized maximum likelihood approach for estimating functions and parameters of interest is described. In the second part we explore a semiparametric marginal modeling

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... rk appropriate for correlated ordinal responses. We model the marginal response probabilities and pairwise association structure by t wo semiparametric regressions. To estimate the model we derive an algorithm which is based on penalized generalized estimating equations. This nonparametric approach allows to estimate the marginal model without specifying the entire distribution of the correlated response. The methods are illustrated by t wo applications concerning the attitude toward smoking restrictions in the workplace and the state of damage in a Bavarian forest district.