Decays Of Xc0,2 -> omega omega are observed for the first time using a sample of 14.0 x 10(6) Psi(2S) events collected with the BESII detector. The branching ratios are determined to be B(Xc0 -> omega omega) = (2.29 +/- 0.58 +/- 0.41) x 10(-3) and B(Xc2 -> omega omega = (1.77 +/- 0.47 +/- 0.36) x 10(-3), where the first errors are statistical and the second systematic. The significances of the two signals are 4.4 sigma and 4.7 sigma, respectively. (c) 2005 Elsevier B.V. All rights reserved.