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Quantum deformations of D=4 Lorentz, Poincare and super-Poincare algebras are discussed. In the case of Poincare algebra the total list of the classical r-matrices obtained by S.Zakrzewski, which satisfy the homogeneous classical Yang-Baxter equation, consists of 21 cases. These r-matrices have various numbers of free parameters and almost all of them can be presented as a sum of subordinated r-matrices of Abelian and Jordanian types. Almost all r-matrices of S. Zakrzewski list for the Poincare algebra can be extend to the Poincare superalgebra. Corresponding twists describing quantum deformations are given in explicit form.