In this article we explain how the existing linear response theory of time-dependent density-functional theory can be extended to. obtain excitation.,energies in the framework of time-dependent current-density-functional theory. We use the Vignale-Kohn current-functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchange-correlation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The pi*<--pi transitions obtained with the Vignale-Kohn functional are in good agreement with experiment and other theoretical results and they are in general an improvement upon the adiabatic local density approximation. In case of the pi*<--n transitions the Vignale-Kohn functional fails, giving results that strongly overestimate the experimental and. other theoretical results. The benchmark set also contains some other types of excitations for which no clear failures or improvements are observed. (C) 2004 American Institute of Physics.