Continuous data can be analyzed with ordinal cumulative probability models (CPMs), also known as 'cumulative link models.' These models belong to the class of semiparametric linear transformation models, where the data are assumed to follow a known linear model after some unspecified transformation that is empirically estimated. CPMs have many benefits including that they are able to handle a wide variety of data types; they can readily address detection limits; they are invariant to monotonic transformations of the response variable; and they model the cumulative distribution function from which conditional expectations, quantiles, probability indices, and other interpretable parameters are easily derived. To date, most research with these models has focused on cross-sectional data. We investigate the use of CPMs with repeated measures longitudinal data. We describe extensions of these models using generalized estimation equations approaches, and we discuss computational challenges.