For the development of levitation bearings and transportation systems based on coated conductor (CC) tapes it is important to know not only information on levitation force at vertical displacement, but also the data on stability of the system during lateral displacements of superconductor relative to permanent magnets. In this paper, we present new experimental results on investigation of both levitation and guidance forces of CC-tapes stacks subjected to cyclical lateral displacements relative to the position of permanent magnet. For the measurements we used 12 mm wide commercially available CC-tape manufactured by SuperOx. The long tape was cut into pieces 12 mm × 12 mm which then put to the stack. Total number of the single tape in the stack N was varied from 5 to 100. Under lateral displacement we measured the dependencies of levitation and guidance forces on value of displacement for various number of N and found that both levitation and guidance forces tend to decrease as a number of periodical cycles of displacements increase. The rate of reducing of forces was observed to depend on the number of tapes in the stack. We observed that dependencies of levitation and lateral forces on lateral displacements have a hysteresis. The area of hysteresis, which corresponds to the magnitude of energy losses, was found to decrease with increasing of number of elements in the stack. Experimental results are in a good agreement with the theoretical calculations of lateral force.