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Abstract We present an interacting system of equations with sixteen supersymmetries and an SO(2) × SO(6) R-symmetry where the fields depend on two space and one null dimensions that is derived from a representation of the six-dimensional (2, 0) superalgebra. The system can be viewed as two M5-branes compactified on S − 1 × T 2 $$ {S}_{-}^1\times {\mathbb{T}}^2 $$ or equivalently as M2-branes on ℝ + × ℝ 2 $$ {\mathbb{R}}_{+}\times {\mathbb{R}}^2 $$ , where ± refer to null directions. We show that for a particular choice of fields the dynamics can be reduced to motion on the moduli space of solutions to the Hitchin system. We argue that this provides a description of intersecting null M2-branes and is also related by U-duality to a DLCQ description of four-dimensional maximally supersymmetric Yang-Mills.