We present a criterion of the stability of a polymeric blend of two species in terms of the three different interaction parameters between the same or different monomeric units. Long chain correlations among different chains are taken into account by including the contribution from all configurations having one loop. The special cases of chemically identical polymers of different size where all three interaction parameters become the same can be deduced and compared with that of different polymers. The stability limits of the system is analyzed in the three dimensional (3D) and in the two dimensional (2D) space in order to describe the behavior of a blend in the bulk and in a thin film where the 2D character of the chains is increased. Going from the 3D to the 2D case while the stability of a system of chemically identical homopolymers of different size decreases that of two different homopolymers increases but may decrease too. (C) 2003 American Institute of Physics.