  In this paper we consider Chevalley groups over commutative rings with $1$,
constructed by irreducible root systems of rank $>1$. We always suppose that
for the systems $A_2, B_\ell, C_\ell, F_4, G_2$ our rings contain $1/2$ and for
the system $G_2$ also $1/3$. Under these assumptions we prove that the central
quotients of Chevalley groups are regularly bi-interpretable with the
corresponding rings, the class of all central quotients of Chevalley groups of
a given type is elementarily definable and even finitely axiomatizable. The
same holds for adjoint Chevalley groups and for other Chevalley groups with
some special condition of bounded generation. We also give an example of
Chevalley group with infinite center, which is not bi-interpretable with the
corresponding ring and is elementarily equivalent to a group that is not a
Chevalley group itself.
