The method of structure-oriented lumping (SOL) for describing the compositions, chemical reactions, and properties of complex hydrocarbon mixtures has been extended to molecules found in vacuum residua. The SOL approach was initially developed for gas oil and lighter fractions (i.e., those boiling at < 1100 degrees F), where molecular compositions can be organized in terms of homologous series of single-core molecules (e.g., benzene and alkylated benzenes). In this work, residua molecules are represented as multicore molecules comprising linked assemblies of single-core species. The original SOL molecular description, using vectors of structural increments, is retained, along with the addition of information about the core linkages, and the extension meshes seamlessly with the conventional SOL notation. Using this formalism, properties of residua may be readily calculated and kinetic models of residua conversion processes developed.