A new approach to many-body quasiparticle dynamics of the Anderson impurity model at flnite temperatures is proposed in the framework of the equation-of-motion method. We flnd a new exact identity, which relates the one-particle and many-particle Green functions. Using this identity, it is shown that a new interpolating approximation for the one-particle Green function can be constructed. The approximation which simultaneously reproduces tle weak-coupling limit and the strong coupling limit can be formulated self-consistently. This approach offers a new method for a systematic construction of the approximate interpolating dynamical solutions of strongly correlated electron models.PACS numbers: 67.40. Db, 71.28.+d, 75.20.Hr The problem of an adequate description of strongly correlated electron systems has been studied intensively for the last decade, especially in the context of heavy fermions and high-Τ superconductivity [1]. Theoretical description of strongly correlated electron systems involves simplifled model Hamiltonian. These includes as workable patterns single-impurity Anderson model (SIAM) and Hubbard model. Recently, a lot of effort has been made to gain a better insight into the dynamical properties of the Anderson/Hubbard model [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], especially in the context of many impurities case (e.g. [6]). This field is quite important for description of magnetic properties of anomalous rare-earth compounds [8]. The problem of an adequate and consistent description of dynamics of single-impurity and twoimpurity Anderson models (SIAM and TIAM) and other models of correlated 1attice electrons has not been fully analytically solved yet. The present paper is primarily devoted to the analysis of the relevant many-body dynamical solution of the SIAM and its correct functional structure. We wish to determine which solution actually arises from both the self-consistent many-body approach and intrinsic nature of the model itself. The Hamiltonian of SIAM has the standard form. We will consider single-particle GF of localized electrons. To improve (355) '