This paper considers finite mixtures of structural equation models with non-linear effects of exogenous latent variables and non-recursive relations among endogenous latent variables. A Bayesian approach is developed to analyse this kind of model. In order to cope with the label switching problem, the permutation sampler is used to choose an appropriate identification constraint. Furthermore, a hybrid Markov chain Monte Carlo method that combines the Gibbs sampler, Metropolis–Hastings algorithm, and Langevin–Hastings algorithm is implemented to produce the Bayesian outputs. Finally, the proposed approach is illustrated by a simulation study and a real example.