Time-resolved optical spin orientation is employed to study spin dynamics of I * and I * 1 excitons bound to isoelectronic centers in bulk ZnO. It is found that spin orientation at the exciton ground state can be generated using resonant excitation via a higher lying exciton state located at about 4 meV from the ground state. Based on the performed rate equation analysis of the measured spin dynamics, characteristic times of subsequent hole, electron, and direct exciton spin flips in the exciton ground state are determined as being τ s h = 0.4 ns, τ s e 15 ns, and τ s eh 15 ns, respectively. This relatively slow spin relaxation of the isoelectronic bound excitons is attributed to combined effects of (i) weak e-h exchange interaction, (ii) restriction of the exciton movement due to its binding at the isoelectronic center, and (iii) suppressed spin-orbit coupling for the tightly bound hole.