In this paper we consider the nonlinear superposition operator $F$ in $l_p$ spaces of sequences, generated by the function \[ f(s,u)=a(s)+u^n\qquad\text{or}\qquad f(s,u)=a(s)\cdot u^n \] First we show that these operators are Fr\'echet differentiable. Then we find out the Neuberger spectra $\sigma_N(F)$ of these operators. We compare it with some other nonlinear spectra and indicate some possible applications.