Third order iterative methods without using second Frechet derivative Summary: Third order iterative methods without using second Fr´echet derivative Great quantity of general problems may be reduced to Ţnding zeros. The roots of a nonlinear equation cannot in general be expressed in closed form. Thus, in order to solve nonlinear equations, we have to use approximate methods. One of the most important techniques to study these equations is the use of itera- tive processes, starting from an initial approximation x0, called pivot, successive approaches (until some predetermined convergence criterion is satisŢed) xi are computed , i = 1, 2, . . . , with the help of certain iteration function : X X, xi+1 := (xi), i = 0, 1, 2 . . . (1) Certainly Newton's method is the most useful iteration for this purpose. The advance of computational techniques has allowed the development of some more complicated iterative methods in order to obtain greater order of convergence as Chebyshev and Halley methods. In these methods we have to evaluate Ţrst and overall second derivatives. These difficulties are usually harder than the advantage because of the order of these methods. So, two order iterative methods are widely used. In this paper, we present a modiŢcation of classical third order iterative me- thods. The main advantage of these methods is they do not need evaluate any second derivative, but having the same properties of convergence than the classical Collections: Mathematics