Adaptive predictors in signal processing and control are mostly based on autoregresive models with external inputs (ARX). There are, however, applications for which the liminations of ARX models might be significant. When looking for an alternative universal class of models, finite order Markov chains seem to be promising alternative. However, exponential burst of the transition-table dimensionality with increasing dimension of the data space and memory length restricts applicability of this modeland this problem motivates the search for a feasible approximation. Many methodologies for aggregation-disaggregation (AD) in large Markov chains have been proposed in recent years. However , the addressed AD algorithms are not suitable for on-line adaptive prediction and control. A novel practical AD method is needed in order to apply MC models to wider fields, especially adaptive systems working permanently in real time. A promising approximation is developed and studied in my PhD thesis.