  We discuss the role of the conservation laws related with U(1) internal
symmetry group in the statistical model description of particle productions in
ultrarelativistic heavy ion collisions. We derive and show the differences in
particle multiplicities in the canonical and the grand canonical formulation of
quantum number conservation. The time evolution and the approach to chemical
equilibrium in the above ensembles is discussed in terms of kinetic master
equation. The application of the statistical model to the description of
(multi)strange particle yields at GSI/SIS and the SPS energies is also
presented.
