We consider the low-energy excitations of one-dimensional spin-orbital models which consist of spin waves, orbital waves, and joint spin-orbital excitations. Among the latter we identify strongly entangled spin-orbital bound states which appear as peaks in the von Neumann entropy (vNE) spectral function introduced in this work. The strong entanglement of bound states is manifested by a universal logarithmic scaling of the vNE with system size, while the vNE of other spin-orbital excitations saturates. We suggest that spin-orbital entanglement can be experimentally explored by the measurement of the dynamical spin-orbital correlations using resonant inelastic x-ray scattering, where strong spin-orbit coupling associated with the core hole plays a role. Introduction.-The spin-orbital interplay is one of the important topics in the theory of strongly correlated electrons [1]. In many cases, the intertwined spin-orbital interaction is decoupled by mean-field approximation, and the spin and orbital dynamics are independent from each other. Thus a spinonly Heisenberg model can be derived by averaging over the orbital state, which successfully explains magnetism and optical excitations in some materials, for instance in LaMnO 3 [2]. But in others, especially in t 2g systems [3], the orbital degeneracy plays an indispensable role in understanding the lowenergy properties in the Mott insulators of transition metal oxides (TMOs), such as LaTiO 3 [4], LaVO 3 and YVO 3 [5], and also in recently discussed RbO 2 [6]. The well known cases are also strong spin-orbit coupling which leads to locally entangled states [7], and entanglement on the superexchange bonds in K 3 Cu 2 F 7 [8]. For such models, the mean-field-type approximation and the decoupling of composite spin-orbital correlations fail and generate uncontrolled errors, even when the orbitals are polarized [9]. The strong spin-orbital fluctuations on the exchange bonds will induce the violation of the Goodenough-Kanamori rules [10]. Furthermore, the flavors may form exotic composite spin-orbital excitations.Model and system.-A paradigmatic model derived for a TMO in Mott-insulating limit is the one-dimensional (1D) spin-orbital Hamiltonian, which reads