Many-body cooperative energy transfer is an important process in biology, medicine, photosynthesis, rare-earth-doped laser materials, responsible for up- and down-conversion of energy, optical excitation sensitization and relaxation. We present an analytical solution for long-time asymptotic of static luminescence quenching kinetics due to cooperative energy transfer to ensembles of acceptors comprised of two-, three-, and more particles. For cooperative energy transfer and cooperative luminescence quenching to n-body acceptors we have discovered a new law of power d/(nS - (n - 1)d) time dependence (d = 1, 2, 3 is the space dimension, S = 6, 8, 10 is the multipolarty of interaction: dipole-dipole, dipole-quadrupole, or quadrupole-quadrupole). The detailed numerical simulation of cooperative quenching by Monte-Carlo method confirms the theoretical result. (C) 2012 Elsevier B.V. All rights reserved.