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We study the properties of the covariant supersymmetric and kappa-symmetricaction for a system of N nearly coincident M0-branes (mM0 system) in flateleven dimensional (11D) superspace and obtain supersymmetric equations forthis dynamical system. Although a single M0-brane is the massless 11Dsuperparticle, center of energy motion of the mM0 system is characterized by anonnegative constant mass M constructed from the matrix fields describing therelative motion of mM0 constituents. We show that a bosonic solution of the mM0equations can be supersymmetric iff this effective mass vanishes, M=0, and thatall the supersymmetric bosonic solutions preserve just one half of the 11Dsupersymmetry.

Covariant action and equations of motion for the eleven dimensional multiple M0-brane system