Abstract Given a φ -function φ and k ∈ ℕ, we introduce and study the concept of ( φ, k )-variation in the sense of Riesz of a real function on a compact interval. We show that a function u :[ a, b ] → ℝ has a bounded ( φ, k )-variation if and only if u ( k− 1) is absolutely continuous on [ a, b ]and u ( k ) belongs to the Orlicz class L φ [ a, b ]. We also show that the space generated by this class of functions is a Banach space. Our approach simultaneously generalizes the concepts of the Riesz φ -variation, the de la Vallée Poussin second-variation and the Popoviciu k th variation.