The first part of this paper investigates the structure of δ-local modules. We prove that the following statements are equivalent for a module M: (i) M is δ-local; (ii) M is a coatomic module with either (a) M is a semisimple module having a maximal submodule N such that N is projective and M/N is singular, or (b) M has a unique essential maximal submodule K ≤ M such that for every maximal submodule L ≠ K, M/L is projective. The second part establishes some properties of finitely generated amply δ-supplemented modules.
