In this paper it is proved that some algebras of integral operators are equivalent to the algebra generated by singular integral operators with piecewise continuous coefficients. Two Banach algebras (subalgebras) A1(½ L(B1) and A2(½ L(B2) will be called equivalent if there exists an invertible operator M 2 L(B1; B2) such that the set of operators of the form MAM¡1 (A 2 A1) coincides with the algebra A2. The notion of symbol is defined for the operators of these algebras by means of equivalence. It is established that the Noetherian conditions and the indices of the operators are expressed by determinant of their symbols. In the study of algebras some fundamental results obtained by mathematicians I. Gohberg and N. Krupnik in [1–3] are used.