The nonlinear parametric interaction of Alfven waves with magnetosonic and ion-acoustic waves is considered on the basis of two-fluid magnetohydrodynamics. A nonlinear dispersion relation describing three-wave interaction, instability growth rate have been calculated and estimated. The analyses of theoretical results shows that kinetic effects in the Alfven waves (the finite ion Larmour radius) are essential for the parametric interactions of waves. Nonlinear parametric processes studied in the paper could take place in the solar coronal loops, where plasma parameter is small. The products of the decay-magnetosonic and ion-acoustic waves, can effectively heat the coronal plasma in consequence of rapid dissipation. ©2000 American Institute of Physics.