The Kondo semiconductor YbB12 exhibits a spin and charge gap of approximately 15 meV. Close to the gap energy narrow dispersive collective excitations were identified by previous inelastic neutron scattering experiments. We present a theoretical analysis of these excitations. Starting from a periodic Anderson model for crystalline electric field (CEF) split 4f states we derive the hybridized quasiparticle bands in slave boson mean-field approximation and calculate the momentum dependent dynamical susceptibility in random phase approximation (RPA). We show that a small difference in the hybridization of the two CEF (quasi-) quartets leads to the appearance of two dispersive spin resonance excitations at the continuum threshold. Their intensity is largest at the antiferromagnetic (AF) zone boundary point and they have an upward dispersion which merges with the continuum less than halfway into the Brillouin zone. Our theoretical analysis explains the most salient features of previously unexplained experiments on the magnetic excitations of YbB12.The so-called Kondo insulators or semiconductors like, e.g., CeNiSn, SmB 6 and YbB 12 represent a special class of strongly correlated electrons [1]. In these compounds the conduction electrons hybridize with nearly localized 4f electrons. The Coulomb repulsion of the latter results in a small energy gap[2] of order 10 meV at the Fermi level [3,4].At temperatures higher than the gap energy these materials behave like Kondo metals exhibiting their typical spin fluctuation spectrum. But a low temperatures a spin and charge gap opens indicating the formation of an insulating singlet ground state [1,5]. This may be concluded from the total suppression of the local moment in the susceptibility and from the semiconducting behavior of the resistivity, respectively [6]. The gap formation may also be seen directly in the dynamical susceptibility and finite frequency conductivity as probed in inelastic neutron scattering (INS) and optical conductivity experiments. In cubic YbB 12 the spin [7] and charge [8] gap obtained in this way are approximately equal to 15 meV but in general they need not be identical.In addition unpolarized [9] and polarized [7] INS has found an interesting dispersive fine structure around this threshold energy. Three excitation branches have been identified with energies 15, 20 and 38 meV, respectively by analyzing the spectral function of the dynamical susceptibility. Since the lower two INS peaks are narrow and mostly centered at the zone boundary L-point with Q = (π, π, π) they may be associated with the formation of a collective heavy quasiparticle spin resonance exciton appearing around the spin gap threshold [7,9] and driven by heavy quasiparticle interactions. The collective modes remain visible in the 20 meV region up to T = 159 K [10,11]. Similar spin resonance phenomena appear as result of feedback effect in unconven-tional heavy-fermion superconductors below the quasiparticle continuum threshold at 2∆ 0 where ∆ 0 is the gap amplitude[12]. The upper p...