  We show that infinite variety of Poincar\'{e} bialgebras with nontrivial
classical r-matrices generate nonsymmetric nonlinear composition laws for the
fourmomenta. We also present the problem of lifting the Poincar\'{e} bialgebras
to quantum Poincar\'{e} groups by using e.g. Drinfeld twist, what permits to
provide the nonlinear composition law in any order of dimensionfull deformation
parmeter $\lambda$ (from physical reasons we can put $\lambda = \lambda_{p}$
where $\lambda_{p}$ is the Planck lenght). The second infinite variety of
composition laws for fourmomentum is obtained by nonlinear change of basis in
Poincar\'{e} algebra, which can be performed for any choice of coalgebraic
sector, with classical or quantum coproduct. In last Section we propose some
modification of Hopf algebra scheme with Casimir-dependent deformation
parameter, which can help to resolve the problem of consistent passage to
macroscopic classical limit.
