  For many real physico-chemical complex systems detailed mechanism includes
both reversible and irreversible reactions. Such systems are typical in
homogeneous combustion and heterogeneous catalytic oxidation. Most complex
enzyme reactions include irreversible steps. The classical thermodynamics has
no limit for irreversible reactions whereas the kinetic equations may have such
a limit. We represent the systems with irreversible reactions as the limits of
the fully reversible systems when some of the equilibrium concentrations tend
to zero. The structure of the limit reaction system crucially depends on the
relative rates of this tendency to zero. We study the dynamics of the limit
system and describe its limit behavior as $t \to \infty$. If the reversible
systems obey the principle of detailed balance then the limit system with some
irreversible reactions must satisfy the {\em extended principle of detailed
balance}. It is formulated and proven in the form of two conditions: (i) the
reversible part satisfies the principle of detailed balance and (ii) the convex
hull of the stoichiometric vectors of the irreversible reactions does not
intersect the linear span of the stoichiometric vectors of the reversible
reactions. These conditions imply the existence of the global Lyapunov
functionals and alow an algebraic description of the limit behavior. The
thermodynamic theory of the irreversible limit of reversible reactions is
illustrated by the analysis of hydrogen combustion.
