This paper presents a new family of two-step iterative methods as a new modication to the Halley's method. Also a
family of one-step iterative methods is generated using the variational iteration technique to approximate the multiple roots
of nonlinear equations with unknown multiplicity . The order of convergence is analyzed and proved that, some of the
proposed methods reach the optimal order of convergence, which is higher than that of Newton0s method. The outcomes
for some numerical examples are given to approve the eciency of the presented methods compared with some other known
methods. Mathematics Subject Classication: 34A45, 34A45, 37N30.