Using non-Hermitian realizations of SU(1, 1) Lie algebra in terms of an f-oscillator, we generalize the notionof nonlinear coherent states to the single-mode and two-mode nonlinear SU(1, 1) coherent states. Taking the nonlinearityfunction f(k) = Llk(η2)[(k + 1)Lok (η2)]-1, their statistical properties are studied.