A variety of locally dependent models are introduced having individual difference parameters that may be interpreted as reflecting effective learning abilities. One version is a univariate extension of the Rasch model with a Markov property: the probability that a given individual will pass an item depends on previous items only through the immediately preceding item score. Another version is a bivariate extension of the above Rasch Markov model, yielding separable "aptitude" and "learning ability" parameters. For both models, necessary derivatives are presented that are associated with maximum likelihood as well as certain ad hoc estimation procedures. A small number of simulated as well as analytical accuracy results for the estimation procedures are also provided. (Author)