A continuation method is any procedure which starting from X that produces an acceptable approximations Xk of a sequence of parameter values λ1 ,λ2,• • • λn so aa continuation methods are discussed in this thesis in the broad sense as algorithms for the computational analysis of specified parts of a solution of a nonlinear system of equations of the form, FX = 0, where F: Rm —> Rn is a given mapping and m > n . In this thesis we analysis the case m = n +1 based on the theory in evaluating the tangent and steplength. Another simple method has been developed. Numerical results are obtained by solving several examples. Our conslutions infavier with the continuation methods which becomes increasingly important tools for solving a nonlinear system of equations and for finding an approximate solution to the integral equations and to the nonlinear boundary value problems.