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We consider the 2D Hubbard model in the strong-coupling case (U>>W) and atlow electron density (nd^2<<1). We find an antibound state as a pole in thetwo-particle T-matrix. The contribution of this pole in the self-energyreproduces a two-pole structure in the dressed one-particle Green-functionsimilar to the Hubbard-I approximation. We also discuss briefly theEngelbrecht-Randeria mode which corresponds to the pairing of two holes belowthe bottom of the band for U>>W and low electron density. Both poles producenon-trivial corrections to Landau Fermi-liquid picture already at low electrondensity but do not destroy it in 2D

Manifestation of the Upper Hubbard band in the 2D Hubbard model at low electron density