In this paper we address the problem of the adaptation of a speech recognition system to a new environment. The aim of adaptation is to compensate the mismatch between training and testing conditions without retraining completely the recognition system. The questions are what has to be compensated and how? We propose to compensate the means and variances of the Gaussian pdfs, representing the acoustic models, using the linear transformations and ML and MAP estimations. To better take into account the variability of the adaptation data, the pdfs of models are organised in a tree. This tree structure is used also for the definition of prior densities of transformations. The approach is called Structural Maximum a Posteriori adaptation (SMAP). SMAP is developed for a segment-based model, the Mixture Stochastic Trajectory Model (MSTM). Experimental results on RM task for supervised speaker adaptation show that SMAP significantly outperforms the MLLR adaptation for the same amount of adaptation data and the same number of transformation parameters.