We consider two new classes of twisted D=4 quantum Poincar\'{ e} symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincar\'{ e} algebras which provide the examples of Lie-algebraic noncommutativity of the translations. The corresponding associative star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the twist deformations of Poincar\'{ e} symmetries generated by the twist with its carrier in Lorentz algebra. We describe corresponding deformed Poincar\'{ e} group which provides the quadratic deformations of translation sector and define the quadratically deformed Minkowski space-time algebra.
Categories: hep-th