NEARBY clusters of galaxies are filled with red elliptical ’E’ and lenticular ’S0’ galaxies(1), while younger clusters (at redshifts of greater than or similar to 0.4) contain substantial populations of blue spiral galaxies with morphological peculiarities(2-7) (see Fig. 1), Thus, within the last 4-5 billion years, galaxies in clusters underwent strong evolution that completely changed their character, By contrast, galaxies that are not associated with clusters show far less morphological evolutions(8). Here we propose that multiple highspeed encounters between galaxies-’galaxy harassment’-drives the morphological evolution in clusters, Our simulations show that these encounters are very different from mergers; they transform small disk galaxies into dwarf elliptical or dwarf spheroidal galaxies, Harassment will leave detectable debris arcs and could provide fuel for quasars in sub-luminous host galaxies.