  A parametric approach is developed to the method of S-tree diagrams and its
generalization for investigation of the hierarchical substructure of $N$-body
nonlinearly interacting systems (e.g., clusters of galaxies). The introduction
of a parametric function allows us to take into account the individual features
of the particles which do not have a direct influence on the dynamics of the
system but are crucial for analyzing the output data. An algorithm is proposed
for the latter based on the construction of parametrical subgroups.
  A generalization of the S-tree scheme is presented as well. This enables us
to perform parallel substructure analysis with respect to various dependent or
independent parameters, thus using fully the initial information of a system.
