A Systematic Approach to Anomalous Phenomena at High Energies

In one-dimensional case the search for presence of the anomalous phenomena in multiplicity distributions is usually performed in frame of the horizontal, vertical and mixed types of the analysis. We show that if the data involve a d-dimensional phase space, there exists a convenient procedure, generalizing the one-dimensional approach, which allows to introduce more non-trivial types of the analysis; we formulate them in some detail in one-, two-, and partially also in three-dimensions.