The notions of (transitive, commutative, antisymmetric) bordered GE-algebras are introduced, and their properties are investigated. Relations between bordered GE-algebras and bounded Hilbert algebras are stated. The concept of duplex bordered GE-algebras is introduced, and its properties are investigated. Relations between antisymmetric bordered GE-algebras and duplex bordered GE-algebras are discussed. A characterization of duplex bordered GE-algebras is provided. A new class of bordered GE-algebras called cross bordered GE-algebras, which generalizes the class of duplex bordered GE-algebras, is introduced, and its properties are investigated. Relations between duplex bordered GE-algebras and cross bordered GE-algebra are considered. \par The motivation and details of this article are very clear. The results are interesting.