The λ_⇑-calculus is a confluent first-order term rewriting system which contains the λ-calculus written in de Bruijn's notation. The substitution is defined explicitly in λ_⇑ by a subsystem, called the σ_⇑-calculus. In this paper, we use the σ⇑-calculus as the substitution mechanism of general higher-order systems which we will name Explicit Reduction Systems. We give general conditions to define a confluent XRS. Particularly, we restrict the general condition of orthogonality of the classical higher-order rewriting systems to the orthogonality of the rules initiating substitutions.