When a suitable partial ordered relation is attached to a Γsemihyperring, it results into an ordered Γ-semihyperring. Concepts of an ordered Γ-semihyperring, Γ-band, idempotent Γ-semihyperring, totally ordered Γ-semihyperring, positively ordered Γ-semihyperring, negatively ordered Γ-semihyperring are introduced which are useful to study derivation on ordered Γ-semihyperrings. Derivation is nothing but an additive mapping fulfilling the Leibniz rule. In this paper, we introduce the concept of (σ, τ)-derivation which is a generalization of σ-derivation and derivation on Γ-semihyperring and study some properties of (σ, τ)-derivation on an ordered Γ-semihyperring. Some results reflecting different natures of (σ, τ)-derivation depending on natures of the endomorphisms are encountered.