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In this talk, we present the band gap formation and the existence of localized nonlin ear modes of the underlying nonlinear Schr(o)dinger equation (NLS) with two dimensional irregular lattices, possessing dislocations, defects and quasicrystal structures.We next in vestigate vortex solitons on quasicrytal lattices.We use a spectral fixed-point numerical scheme to obtain the nonlinear localized modes and vortex solitons.By using direct computational simulations, stability properties of fundamental and vortex solitons are investigated.