This paper proposes a generalization of the nonlinear simultaneous equation model of Pesaran and Pick (2007) by modelling the comovement between the two endogenous variables as a smooth function of the magnitude of the endogenous variable rather than a step function. The threshold and the speed at which a shock is transmitted are estimated with the other parameters of the model. We investigate the properties of an accurate estimation method which takes into account endogeneity, and a testing procedure for simultaneity in the presence of nuisance parameters under the null hypothesis. We study the conditions on the parameters that ensure the uniqueness of the implicit reduced form of the model. We apply this methodology to the comovement between the sovereign and banking sectors of nine developed countries.