We predict theoretically that nanoparticles of octupolar symmetry (nanotriangles and nanotetrahedra), whose orientation cannot be affected by means of linear optics, subjected to a coherent mixture of fundamental and second harmonic fields will rotate and orient controlled by the relative phase between these fields. This is due to the generation of the second-harmonic polarization and its interaction with the second-harmonic field. We have described this effect quantitatively for triangular and tetrahedral clusters of metal nanospheres where it can be observed experimentally and used in applications. (c) 2006 Elsevier B.V. All rights reserved.