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This article discusses the problem of estimation of parameters in finite mixtures of regression models when the error distributions are assumed to be symmetric about zero and independent of predictors.We refer to these mixtures as semi-parametric because no additional assumptions other than symmetry are made regarding the parametric form of the error distributions.We develop a notion of identifiability of finite mixture of regression models,and sufficient conditions for identifiability of parameters.We propose a distance-based method for estimating the parameters of the regression function and establish the strong consistency and asymptotic normality of the estimator.