Wiener models, which consider a linear dynamical model and a nonlinear output map, can represent a wide range of industrial processes. In this paper, observer design approaches for these systems are proposed. The approaches consider a Wiener structure having a Lipschitz nonlinear perturbation term and explicit and implicit nonlinear output maps. The observers gain are obtained by solving a set of LMIs which consider the Lipschitz constant associated to the nonlinear perturbation and the convex hull associated to the output map derivative. A conductivity tracking problem and pH neutralization processes illustrate the main features of the design process and the performance obtained with the proposed design approach.