Abstract. In this paper we treat the problem of subsurface characterization of a fractured porous medium. We begin by introducing the surrogate dual porosity, dual permeability model for tracer flow. We next introduce the Markov chain Monte Carlo (MCMC) method to be used within a framework where a number of permeability samples are considered. The acceptance criteria for our problem is built in the Bayesian statistical framework and is enforced through sampling from the posterior distribution of the permeability fields conditioned to dynamic tracer cut data. In order to sample from the distribution we must solve a series of problems which requires a fine scale solution of the dual model. As direct MCMC is a costly method with a low acceptance rate, we introduce a two-stage MCMC alternative which requires a suitable coarse scale solution method of the dual model. With this filtering process we are able to decrease our computational time as well as increase the proposal acceptance rate. A number of numerical examples are presented to illustrate the performance of the method.