The notions of coupled N-subalgebra, coupled (positive implicative) N-ideals of $d$-algebras are introduced, and related properties are investigated. Characterizations of a coupled $mathcal{N}$-subalgebra and a coupled (positive implicative) $mathcal{N}$-ideals of $d$-algebras are given. Relations among a coupled $mathcal{N}$-subalgebra, a coupled $mathcal{N}$-ideal and a coupled positive implicative $mathcal{N}$-ideal of $d$-algebras are discussed.