This paper deals with the Riemann-Hilbert boundary value problem for nonlinear elliptic complex equations ofnorder in simply and multiply connected domains. Firstly we give the formulation of the Riemann-Hilbert problem and its well posedness and then we give the representation of solutions for the modified boundary value problem and prove its solvability, and finally derive solvability conditions of the original Kiemaiin-Hilbert problem. In the following, we divide into two cases of complex equations of2nth order and2n+ 1th order to discuss.