We study the resonance energy transfer between parallel neighboring organic and semiconductor quantum wires which is caused by the resonance dipole-dipole interaction between the wires. Due to this interaction, a new hybrid excited state arises which is a mixture of Frenkel and Wannier-Mott excitons. For the transition dipole moments oriented perpendicular to the wires, the interwire hybridization strength is nonzero even for small exciton wavevectors along the wires and decays rather slowly with increasing interwire spacing. This is in contrast to two-dimensional quantum wells where the dipole-dipole coupling decays fast with the increasing interwell distance and takes place only for nonzero excitonic wavevectors. The hybrid wire excitons possess both a large radius and a relatively large oscillator strength which might be especially interesting for the nonlinear optics.