The Time Dependent Density Functional Theory (TD-DFT) method implemented in the ADF program has been extended to treat core electrons excitations. The scheme consists to reduce the complete one-electron excited configurations space to the subspace where only the core electrons are excited. The scheme has been applied to the Ti 1s, Ti 2p and Cl 2p core excitations of TiCl4, employing different basis sets and exchange correlation potentials. The comparison with the experimental data is good, especially for the Ti 2p shell which cannot be described even qualitatively by the too simple Kohn-Sham method. Also the Cl 2p shell, dominated by Rydberg features, is properly described. The method is computationally economic, and can be applied to larger and less symmetric systems. Further extensions to the relativistic case, with explicit spin-orbit treatment, are suggested to improve the description of spin-orbit splitting and intensity redistributions. (C) 2003 Elsevier Science B.V. All rights reserved.