International audienceThis paper proposes a \probabilistic" extension of conditional preference networks as a way to compactly represent a probability distributions over preference orderings. It studies the probabilistic counterparts of the main reasoning tasks, namely dominance testing and optimisation from the algorithmical and complexity viewpoints. Efficient algorithms for tree-structured probabilistic CP-nets are given. As a by-product we obtain a lineartime algorithm for dominance testing in standard, tree-structured CP-nets
