Before revision: This report is about finding clusters of complex solutions of triangular systems of polynomial equations. We introduce the local solution clustering problem for a system of polynomial equations, that is grouping all its complex solutions lying in an initial complex domain in clusters smaller than a given real number \epsilon^n, for any given \epsilon} > 0, and counting the sum of multiplicities of the solutions in each cluster.
After revision: This paper gives the first algorithm for finding a set of natural \epsilon-clusters of complex zeros of a triangular system of polynomials within a given polybox in \mathbb{C^n, for any given \epsilon} > 0, and counting the sum of multiplicities of the solutions in each cluster.