We discuss the definition of particle velocity in doubly special relativity theories. The general formula relating the velocity and four-momentum of the particle is given.

The classical r-matrix for the N=1 super-Poincare algebra, given by Lukierski et al. (1993), is used to describe the graded Poisson structure on the N=1 Poincare supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the super-Poincare group with the deformation parameter q described by the fundamental mass parameter K (K^-1=In q). The K-deformation of N=1 superspace as dual to the K-deformed supersymmetry algebra is discussed.