  We discuss chemical equilibration of particles carrying non-vanishing quantum
numbers related with U(1) internal symmetry. We construct the transport
equation for the time evolution of particle multiplicities and their
probability functions. The solution of these equations is obtained in different
limiting cases. It is argued that a U(1) charged particles, dependent on
thermal conditions inside a fireball, approaches different equilibrium limits.
The differences between kinetics of abundantly and rarely produced particles
are explained.

High Energy Physics - Phenomenology