In this article, we present a generalization of the Bayesian methodology introduced by Cepeda and Gamerman (2001 Cepeda , E. C. , Gamerman , D. ( 2001 ). Bayesian modeling of variance heterogeneity in normal regression models . Brazilian Journal of Probability and Statistics 14 : 207 – 221 . [Google Scholar]) for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm.