For the polyacenes series from naphthalene to hexacene, we present the vertical singlet excitation energies 1 L-1(a) and L-1(b), as well as the first triplet excitation energies obtained by the all-order constricted variational density functional theory with orbital relaxation (R-CV(infinity)-DFT). R-CV(infinity)-DFT is a further development of variational density functional theory (CV(infinity)-DFT), which has already been successfully applied for the calculation of the vertical singlet excitation energies L-1(a) and L-1(b) for polyacenes,(15) and we show that one obtains consistent excitation energies using the local density approximation as a functional for singlet as well as for triplet excitations when going beyond the linear response theory. Furthermore, we apply self-consistent field density functional theory (Delta SCF-DFT) and compare the obtained excitation energies for the first triplet excitations T-1, where, due to the character of the transition, Delta SCF-DFT and R-CV(infinity)-DFT become numerically equivalent, and for the singlet excitations L-1(a) and 1 L-1(b), where the two methods differ.