Let \(\sigma\), \(\tau\) be a pair of types of torsion-free (abelian) groups of rank 1 which are determined by characteristics \((k_ p)\), \((m_ p)\) such that \(k_ p\leq m_ p\) for all primes \(p\). A torsion-free group \(A\) of finite rank \(n\) belongs to the class \(D^{\tau}_{\sigma}\) iff there exists a free subgroup \(J\) of rank \(n\) of \(A\) such that any \(p\)-primary component of \(A/J\) is a direct sum of \(n\) groups isomorphic either to \(Z(p^{k_ p})\) or to \(Z(p^{m_ p})\). For primes \(p\) such that \(k_ p