A fast, low memory cost, Krylov-space-based algorithm is proposed for the diagonalization of large Hamiltonian matrices required in time-dependent Hartree-Fock (TDHF) and adiabatic time-dependent density-functional theory (TDDFT) computations of electronic excitations. A deflection procedure based on the symplectic structure of the TDHF equations is introduced and its capability to find higher eigenmodes of the linearized TDHF operator for a given numerical accuracy is demonstrated. The algorithm may be immediately applied to the formally-identical adiabatic TDDFT equations.