Formal models can be found in different computer science domains - they have the advantage to be independent of application domains and of programming languages. ITSs development is usually not based on formal models. Based on automaton theory and on formal descriptions known from modelling and simulation, the formal tutoring process model (tpm) is a formal model for ITSs. The model exists as basic tpm and as adaptive tpm. The extension of the adaptive model is described in the paper. Extended with a temporal dimension, i.e. the 'counter', the static tpm can be used to realize another way of adaptation: the training case can be changed at runtime based on the counter values. This value can count the learner's steps in the training case, it can be interpreted as duration, or as validity of a state.
