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Equations of motion for M2- and M5-branes are written down in the $E_{11}$current algebra formulation of M-theory. These branes correspond to currents ofthe second and the fifth rank antisymmetric tensors in the $E_{11}$representation, whereas the electric and magnetic fields (coupled to M2- andM5-branes) correspond to currents of the third and the sixth rank antisymmetrictensors, respectively. We show that these equations of motion have solutions interms of the coordinates on M2- and M5-branes. We also discuss the geometricequations, and show that there are static solutions when M2- or M5-brane existsalone and also when M5-brane wraps around M2-brane. This situation is realizedbecause our Einstein-like equation contains an extra term which can beinterpreted as gravitational energy contributing to the curvature, thusavoiding the usual intersection rule.

M2- and M5-branes in E11 Current Algebra Formulation of M-theory