Vibrational state total relaxation rate coefficients, k(nu '') (M), for KH (nu '' = 14-23) by M = H-2 and N-2 have been investigated in an overtone pump-probe configuration. At nu '' = 14, 15, 16 and 17, the rate coefficients k(nu '') (M) increase linearly with vibrational quantum number. The region (nu '' = 18, 19, 20 and 21) where the dependence is much stronger than linear has significant contribution from multiquantum (Delta nu >= 2) relaxation. For nu '' = 18, 19,20 and 21, 0.25. 0.31, 0.38 and 0.31 of the initially prepared population undergo two-quantum (Delta nu = 2) vibrational relaxation in KH (nu '') + H-2 collisions. In KH (nu '') + N-2, the time profile of nu '' = 14(15) after preparation of nu '' = 19(20) was measured. A clear bimodal distribution is observed. The time scale of the first peak is much shorter than the known collisional lifetimes of the intervening vibrational levels and thus a sequential single-quantum relaxation mechanism can be explicitly ruled out. Relaxation of KD with D-2 has been also investigated. The relaxation rate coefficients exhibit distinct maxima for both isotopes (KH and KD). We discuss possible explanation of the experimental results including mass effect. V-R energy transfer and V-V energy transfer. (C) 2012 Elsevier B.V. All rights reserved.