Dipole magnetic moments of several long isotopic chains are analyzed within the self-consistent Finite Fermi System theory based on the Generalized Energy Density Functional method with exact account for the pairing and quasi-particle continuum. New data for nuclei far from the beta-stability valley are included in the analysis. For a number of semi-magic isotopes of the tin and lead chains a good description of the data is obtained, with accuracy of 0.1 - 0.2 mu_N. A chain of non-magic isotopes of copper is also analyzed in detail. It is found that the systematic analysis of magnetic moments of this long chain yields rich information on the evolution of the nuclear structure of the Cu isotopes. In particular, it may give a signal of deformation for the ground state of some nuclei in the chain.
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