  In the paper hereditary classes of ${\rm L}$-structures are studied with
language of the form ${{\rm L} = {\rm L_{fin}} \cup {\rm L_\infty}}$, where
${{\rm L_{fin}} = \langle R_1,R_2,\ldots, R_m, = \rangle}$ and ${{\rm L_\infty}
= \langle R_{m+1}, R_{m+2}, \ldots \rangle}$, and also in ${\rm L_\infty}$ the
number of predicates of each arity is finite, all predicates are ordered in
ascending of their arities and satisfying the property of non-repetition of
elements. A class of ${\rm L}$-structures is called hereditary if it is closed
under substructures. It is proved that class of ${\rm L}$-structures is
hereditary if and only if it can be defined in terms of forbidden
substructures. A class of ${\rm L}$-structures is called universal
axiomatizable if there is a set $Z$ of universal ${\rm L}$-sentences such that
the class consists of all structures that satisfy $Z$. The problems of
universal axiomatizability of hereditary classes of ${\rm L}$-structures are
considered in the paper. It is shown that hereditary class of ${\rm
L}$-structures is universal axiomatizable if and only if it can be defined in
terms of finite forbidden substructures. It is proved that the universal theory
of any axiomatizable hereditary class of ${\rm L}$-structures with recursive
set of minimal forbidden substructures is decidable.
