  Doubly Special Relativity (DSR) theory is a theory with two
observer-independent scales, of velocity and mass (or length). Such a theory
has been proposed by Amelino--Camelia as a kinematic structure which may
underline quantum theory of relativity. Recently another theory of this kind
has been proposed by Magueijo and Smolin. In this paper we show that both these
theories can be understood as particular bases of the $\kappa$--Poincar\'e
theory based on quantum (Hopf) algebra. This observation makes it possible to
construct the space-time sector of Magueijo and Smolin DSR. We also show how
this construction can be extended to the whole class of DSRs. It turns out that
for all such theories the structure of space-time commutators is the same. This
results lead us to the claim that physical predictions of properly defined DSR
theory should be independent of the choice of basis.
