In this paper we investigate structure of the solutions for the MHD flow and heat transfer of an electrically conducting, viscoelastic fluid past a stretching vertical surface in a porous medium, by taking into account the diffusion thermo (Dufour) and thermal-diffusion (Soret) effects. It is shown that the porosity, magnetic, convection and concentration buoyancy effects can be combined within a new parameter called here as a porous magneto-convection concentration parameter. Heat transfer and concentration analysis are also carried out for a boundary process. The physical parameters influencing the flow field are viscoelasticity, porous magneto-convection concentration and suction/injection, and those affecting the temperature field are Prandtl and Dufour numbers, and further affecting the concentration field are Prandtl, Lewis and Dufour numbers. Such parameters greatly alter the behavior of solutions from unique to multiple and determine the boundaries of existence or nonexistence of solutions. The features of the skin friction coefficient, Nusselt number and Sherwood number are also easy to gain from the derived equations. (C) 2013 Elsevier Ltd. All rights reserved.