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Classical adaptation approaches generally allow a reliably trained model to match a particular condition. In this paper, we define an incremental version of the segmental-EM algorithm. This method permits one to incrementally enrich a model first trained with a limited amount of data. Resource memory constraints allow only the initial data statistics to be stored. The proposed method uses these statistics by fixing, within the segmental-EM algorithm applied on both initial and new data, the initial optimal paths in the model for the initial data. We proved theoretically that this is equivalent to the segmental MAP adaptation with specific choice of priors. Experiments on two speaker dependent telephone databases, showed that the approach permitted one to incrementally integrate new conditions of use. The performance was slightly less than that obtained with classical training over the whole data. As expected with the MAP interpretation of the algorithm, initial data characteristics influence largely the model evolution.