A Green's function formalism is used to calculate the energy of impurity modes associated with one and/or two magnetic impurities in the one-dimensional Heisenberg XXZ magnetic chain. The system can be tuned from the Heisenberg to the Ising model varying a parameter 位. A numerical study is performed showing two types of localized modes (s and p). The modes depend on 位 and the degeneracy of the acoustic modes is broken.