We report the implementation of time-dependent density-functional response theory (TD-DFRT) for molecules using the time-dependent local density approximation (TDLDA). This adds exchange and correlation response terms to our previous work which used the density-functional theory (DFT) random phase approximation (RPA) [M. E. Casida, C. Jamorski, F. Bohr, J. Guan, and D. R. Salahub, in Theoretical and Computational Modeling of NLO and Electronic Materials, edited by S. P. Kama and A. T. Yeates (ACS, Washington, D.C., in press)], and provides the first practical, molecular DFT code capable of treating frequency-dependent response properties and electronic excitation spectra based on a formally rigorous approach. The essentials of the method are described, and results for the dynamic mean dipole polarizability and the first eight excitation energies of N-2 are found to be in good agreement with experiment and with results from other ab initio methods.