The recent time-dependent density functional theory approach within the two-component zero order relativistic approximation implemented in the ADF code has been modified in order to treat core electron excitations. The method has been applied to the calculation of the Ti 2p (L-2,L-3) core excitation spectrum in the TiCl4 molecule. The results obtained allow to correctly describe both the L-3 and L-2 manifold of Ti 2p core excited states. Different XC potential have been used in the calculations showing that the results are not very sensitive to the exchange correlation potential choice, provided the asymptotic behaviour is correct. (c) 2005 Elsevier B.V. All rights reserved.