Two hierarchical working equations to calculate the dual descriptor for electronic open-shell systems were deduced based on the formalism of the Conceptual Spin-Polarized Density-Functional Theory (SP-DFT). NO and O-2 molecules were analyzed by taking into account their ground state multiplicities. The NO molecule has been used as a typical conventional example of a system with a doublet multiplicity presenting non-degenerate frontier molecular orbitals and the O-2 molecule has been considered as a typical example of a system with a triplet multiplicity presenting degenerate frontier molecular orbitals. One working equation was tested in carbenes. (C) 2011 Elsevier B.V. All rights reserved.