Summary: Using the periodic unfolding method [see D. Cioraneseu et al., C. R. Acad. Sci., Paris, Sér. I 335, No. 1, 99–104 (2002; Zbl 1001.49016)], we study reiterated homogenization for equations of the form \(-\text{div}(a_\varepsilon (x,Du_\varepsilon))=f\), where \(a_\varepsilon\) is Carathéodory and satisfies some monotone and growth conditions. We show that if we assume that \({\mathcal T}_{\delta (\varepsilon)}'({\mathcal T}_\varepsilon(a_\varepsilon)) (x,y,z,\xi)\) converges, for almost all \((x,y,z)\in\Omega\times Y\times Z\), to a Carathéodory operator, then the sequences \(u_\varepsilon\) and \(Du_\varepsilon\) converge in a certain sense to the solution \((u_0,\widehat u,\widetilde u)\) of a limit variational problem, as \(\varepsilon\to 0\). In particular this contains the case \(a_\varepsilon(x,\xi)= a(x,\frac{x}{\varepsilon}, \frac{\{x/ \varepsilon\}\gamma}{\delta(\varepsilon)},\xi)\), where \(a\) is periodic in the second and third arguments, and continuous in each argument.