Graphene-carbon nanotubes composites were considered as mono- and/or multiderivative structures when both tubes and graphene served either as main bodies or were attached addends. The composites were synthesized computationally in the framework of the unrestricted broken spinsymmetry approach implemented via the Hartree-Fock approximation. Computed profiles of the atomic chemical susceptibility along the tube and across their body as well as over graphene sheets served as quantified pointers that allowed localising the most active contact zones of interacting partners. Two main groups of the composites, conditionally called hammer and cutting-blade structures were considered. Additionally, a particular cradle-like composite is suggested for an individual graphene sheet to be fixed by a pair of nanotubes. Copyright © 2010 American Scientific Publishers All rights reserved.