This paper proposes a macroscopic formulation of coupled heat and mass transfer that can consider non local equilibrium often encountered in biosourced building materials (wood- and plant-fiber based materials). Transferring dual-scale effects and molecular relaxation at the macroscopic level involves a kernel function acting in a convolution product. To ease the computational solution of the set of equations, the memory function is decomposed as a series of exponential functions. Each function yields an internal variable that obeys a simple ordinary differential equation (ODE). This paper first describes the macroscopic and dual-scale formulations used as reference solutions. Subsequently, the modified macroscopic formulation of coupled transfer and its computational solution are presented in detail. The major outcomes of the present study, validated against reference solutions obtained with a comprehensive dual scale model, are as follows: Dual-scale diffusion can be approached accurately by two exponential functions, Even though the dual-scale phenomenon and molecular relaxation do not occur at the same scale, both can be considered in the modified macroscopic formulation of coupled transfer additively, The new macroscopic formulation, together with the computational procedure proposed in this study, can be applied to various configurations, namely coupled heat and mass transfer in packed beds. (C) 2019 Elsevier Ltd. All rights reserved.