  The decays of eta_c to K^+K^-2(pi^+pi^-) and 3(pi^+pi^-) are observed for the
first time using a sample of 5.8X10^7 J/\psi events collected by the BESII
detector. The product branching fractions are determined to be B(J/\psi-->gamma
eta_c)*B(eta_c-->K^+K^-pi^+pi^-pi^+pi^-)=(1.21+-0.32+-
0.23)X10^{-4}$,B(J/\psi-->gamma eta_c)*B(eta_c-->K^{*0}\bar{K}^{*0}pi^+pi^-)=
(1.29+-0.43+-0.32)X10^{-4}$, and (J/\psi-->gamma eta_c)*
B(eta_c-->pi^+pi^-pi^+pi^-pi^+pi^-)= (2.59+-0.32+-0.48)X10^{-4}. The upper
limit for eta_c-->phi pi^+pi^-pi^+pi^- is also obtained as B(J/\psi-->gamma
eta_c)*B(eta_c--> phi pi^+pi^-pi^+pi^-)< 6.03 X10^{-5} at the 90% confidence
level.
