  The hypothesis of local equilibrium (LE) in relativistic heavy ion collisions
at energies from AGS to RHIC is checked in the microscopic transport model. We
find that kinetic, thermal, and chemical equilibration of the expanding
hadronic matter is nearly reached in central collisions at AGS energy for $t
\geq 10$ fm/$c$ in a central cell. At these times the equation of state may be
approximated by a simple dependence $P \cong (0.12-0.15) \epsilon$. Increasing
deviations of the yields and the energy spectra of hadrons from statistical
model values are observed for increasing bombarding energies. The origin of
these deviations is traced to the irreversible multiparticle decays of strings
and many-body $(N \geq 3)$ decays of resonances. The violations of LE indicate
that the matter in the cell reaches a steady state instead of idealized
equilibrium. The entropy density in the cell is only about 6% smaller than that
of the equilibrium state.
