In this paper, we investigate ghost dark energy model in the presence of nonlinear interac- tion between dark energy and dark matter. We also extend the analysis to the so-called generalized ghost dark energy (GGDE) which ρ D = αH + βH 2 . The model contains ) and b 2 (the coupling coefficient of interactions). three free parameters as Ω D , ζ(= 8πGβ 3 We propose three kinds of nonlinear interaction terms and discuss the behavior of equa- tion of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa from JLA catalog, Hubble parameter, baryonic acoustic oscilla- tion and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first nonlinear inter- +0.030 and action, the joint analysis indicates that Ω D = 0.7192 ± 0.0062, b 2 = 0.146 −0.026 ζ = 0.104 ± 0.047 at 1 optimal variance error. For the second interaction, the best fit val- ues at 1σ confidence are Ω D = 0.72091 ± 0.0065, b 2 = 0.0395 ± 0.0080 and ζ ≤ 0.0173. According to combination of all observational data sets considered in this paper, the best fit values for third nonlinearly interacting model are Ω D = 0.7287 ± 0.0062
