A general class of regression models for ordered categorised data is developed and discussed. Thier properties are contrasted with log linear models and other methods of analysis. The general problem of fitting by maximum likelihood is discussed and solved. The models are shown to be multivariate extensions of generalised linear models and the fitting method is iteratively re-weighted least squares. Special attention is given to a particular model--the cumulative logit model--and alternative fitting methods are described for this case. Applications are discussed with the aid of three examples. (Author/GDC)