A semigroup S is a λ- [ρ-, σ-] semigroup if and only if each subsemigroup of S is a left [right, two-sided] ideal of S. Since the concept of ρ-semigroup is the dual of that of λ-semigroup, the results for ρ-semigroups are generally not stated explicitly, σ-semigroups are treated as a special case of λ-semigroups ; in fact, a semigroup S is a σ-semigroup if and only if it is a λ-semigroup and a ρ-semigroup. The purpose of this paper is to determine the structure of λ- [ρ-, σ-] semigroups.