In this paper, a theoretical study is presented for the problem of double-diffusion from a vertical plate embedded in a porous matrix that is saturated with a non-Newtonian (power law) fluid. The study consists of two parts : In the first part, scaling analysis is utilized to obtain estimates of the quantities of interest and to identify the various possible flow regimes depending on the values of the buoyancy ratio and the Lewis number. This task is performed for both the case of a wall with constant temperature and concentration and the case of a wall with constant heat and species flux. In the second part of the study, a numerical solution of the problem is presented for the general case of a wall with arbitrarily varying temperature and concentration. The values of the relevant parameters resulting in a constant heat and species flux or a constant temperature and concentration at the wall are identified. The dependence of the flow, temperature, and concentration fields as well as of the local heat and species fluxes at the wall on the power law exponent, the buoyancy ratio and the Lewis number is documented for the two cases : (a) constant temperature and concentration, (b) constant heat and species flux.