A method for solving the system of nonlinear Fredholm integral equations \[ \phi (x,\lambda)=f(x)+\int^{b}_{a}\Phi (x,y,\phi (y,\lambda))dy \] is discussed, where \(\lambda\) is a sufficiently small parameter, \(\phi\),f,\(\Phi\) are vectors. Using the parameter imbedding method, an equivalent initial value problem for a system of nonlinear coupled integro-differential equations is established. The initial value problem can be reduced to the solution of a system of nonlinear Volterra integral equations which is solvable.