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Abstract: Chaotic breathers of two types are generated in two-dimensional Morse lattices with on-site harmonic potentials. In both a triangular and a square configuration, initial highest-frequency (-mode) disturbances evolve into chaotic breathers. Depending on the magnitude of the parameters in the Morse potential, either quasi-one-dimensional localized chaotic breathers or two-dimensional localized (bell-shaped) ones are numerically observed when the on-site harmonic potential becomes significant. Both types of chaotic breather move irregularly within the lattice, and finally decay out into a thermalization state after a fairly long time. Quasi-one-dimensional localized chaotic breathers are favored as the strength of nonlinearity increases and they decay faster than two-dimensional localized ones. [Copyright &y& Elsevier]