The coupling is investigated of Frenkel-like exciton states formed in a tubular dye aggregate (TDA) to Wannier-Mott-like excitations of a semiconductor nanocrystal (NC). A double well TDA of the cyanine dye C8S3 with a length of 63.4 nm and a diameter of 14.7 nm is considered. The TDA interacts with a spherical Cd819Te630 NC of 4.5 nm diameter. Electronic excitations of the latter are described in a tight-binding model of the electrons and holes combined with a configuration interaction scheme to consider their mutual Coulomb coupling. To achieve a proper description of TDA excitons, a recently determined structure has been used, the energy transfer coupling has been defined as a screened interaction of atomic centered transition charges, and the site energies of the dye molecules have been the subject of a polarization correction. Even if both nanoparticles are in direct contact, the energy transfer coupling between the exciton levels of the TDA and of the NC stays below 1 meV. It results in FRET-type energy transfer with rates somewhat larger than 10(9)/s. They coincide rather well with recent preliminary experiments.