Abstract.The main result is a Young-Stieltjes integral representation of the composition φ • f of two functions f and φ such that for some α ∈ (0, 1], φ has a derivative satisfying a Lipschitz condition of order α, and f has bounded p-variation for some p < 1 + α. If given α ∈ (0, 1], the p-variation of f is bounded for some p < 2 + α, and φ has a second derivative satisfying a Lipschitz condition of order α, then a similar result holds with the Young-Stieltjes integral replaced by its extension.