We present the first fully-nonlinear numerical study of the dynamics of highly spinning black-hole binaries . We evolve binaries from quasicircular orbits ( as inferred from Post-Newtonian theory ) , and find that the last stages of the orbital motion of black-hole binaries are profoundly affected by their individual spins . In order to cleanly display its effects , we consider two equal mass holes with individual spin parameters S / m ^ { 2 } = 0.757 , both aligned and anti-aligned with the orbital angular momentum ( and compare with the spinless case ) , and with an initial orbital period of 125 M . We find that the aligned case completes three orbits and merges significantly after the anti-aligned case , which completes less than one orbit . The total energy radiated for the former case is \approx 7 \% while for the latter it is only \approx 2 \% . The final Kerr hole remnants have rotation parameters a / M = 0.89 and a / M = 0.44 respectively , showing the unlikeliness of creating a maximally rotating black hole out of the merger of two spinning holes .