Before revision:  This paper introduces two classes of semiparametric triangular systems with nonadditively separable unobserved heterogeneity .
After revision: Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric triangular systems with nonadditively separable unobserved heterogeneity .