The new principle of radiation-pressure trapping of neutral dielectric particles by means of alternating light beams was demonstrated in an optical levitation experiment. Stable trapping of micron-sized spheres was observed due to alternating scattering-force fields under conditions where stable cw trapping was not possible. Application of this principle to neutral-atom trapping as a means of circumvention of the optical Earnshaw theorem is suggested. A new stable cw optical trap for spheres was also discovered.