Let G be a module over a ring R, let C = { C i } , i ∈ I \mathcal {C} = \{ {C_i}\}, i \in I , be a family of submodules of G, and let H = { H i } , i ∈ I \mathcal {H} = \{ {H_i}\}, i \in I , where H i {H_i} is a subgroup of Hom R ⁡ ( C i , G ) \operatorname {Hom}_R({C_i},G) with certain properties. To each such pair ( C , H ) (\mathcal {C},\mathcal {H}) , a near-ring M ( C , H ) M(\mathcal {C},\mathcal {H}) is associated, which is a generalization of the near-ring of homogeneous functions determined by (G, R). The transfer of information from module properties of G R {G_R} reflected in ( C , H ) (\mathcal {C},\mathcal {H}) to structural properties of M ( C , H ) M(\mathcal {C},\mathcal {H}) is investigated.