  Recently it was shown that by using two different realizations of
$\hat{o}(1,4)$ Lie algebra one can describe one-parameter standard Snyder model
and two-parameter $\kappa$-deformed Snyder model. In this paper, by using the
generalized Born duality and Jacobi identities we obtain from the
$\kappa$-deformed Snyder model the doubly $\kappa$-deformed Yang model which
provides the new class of quantum relativistic phase spaces. These phase spaces
contain as subalgebras the $\kappa$-deformed Minkowski space-time as well as
quantum $\tilde{\kappa}$-deformed fourmomenta and are depending on five
independent parameters. Such a large class of quantum phase spaces can be
described in $D=4$ by particular realizations of $\hat{o}(1,5)$ algebra, what
illustrates the property that in noncommutative geometry different $D=4$
physical models may be described by various realizations of the same algebraic
structure. Finally, in the last Section we propose two new ways of generalizing
Yang models: by introducing $\hat o(1,3+2N)$ algebras ($N=1,2\ldots$) we
provide internal symmetries $O(N)$ symmetries in Kaluza-Klein extended Yang
model, and by replacing the classical $\hat{o}(1,5)$ algebras which describe
the algebraic structure of Yang models by $\hat o(1,5)$ quantum groups with
suitably chosen nonprimitive coproducts.
