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We investigate the continuity of (α, β)-derivations on B(X)or C*-algebras. We give some sufficient conditions on which (α, β)-derivations on B(X) are continuous and show that each (α, β)-derivation from a unital C*-algebra into its a Banach module is continuous when α and β are continuous at zero. As an application, we also study the ultraweak continuity of (α, β)-derivations on von Neumann algebras.