This paper considers the estimation of Hammerstein models with input saturation. These models are characterised by a linear dynamical model acting on an input sequence which is affected by a hard saturation of unknown level. The main result of the paper lies in a specification of a set of sufficient conditions on the input sequence in order to ensure that a non-linear least-squares approach enjoys properties of consistency and asymptotic normality and furthermore, that an estimate of the parameter covariance matrix is also consistent. The set of assumptions is specified using the concept of near epoch dependence, which has been developed in the econometrics literature. Indeed, one purpose of this paper is to highlight the usefulness of this concept in the context of analysing estimation procedures for nonlinear dynamical systems.