The superposition operator \(Fx(s)=f(s,x(s))\) is the most important operator in nonlinear analysis. There is a vast literature on the theory and applications of this operator in various function spaces; the first systematic study in the Lebesgue function spaces \(L_ p\), for instance, is contained in the book of \textit{M. A. Krasnosel'skii} et al., Integral operators in spaces of summable functions (in Russian), Moscow (1966; Zbl 0145.39703). Very little attention has been given, however, to this operator between sequence space, rather than function spaces. The present paper gives a systematic account of various important properties of the superposition operator in the Lebesgue sequence spaces \(\ell_ p\) (1\(\leq p\leq \infty)\). The authors give conditions (both necessary and sufficient), under which F acts between two spaces \(\ell_ p\) and \(\ell_ q\), is locally bounded, locally continuous, bounded on balls, uniformly continuous on balls, absolutely bounded (i.e. compact), or differentiable. The last section is concerned with an application to a certain ``discrete analogue'' to nonlinear integral equations of Hammerstein type.