In this paper, we have performed ab initio density functional theory calculations to compare the miscibility and magnetic properties of two-dimensional binary surface alloys of the form MxN1-x (M = Fe or Co; N = Pt, Au, Ag, Cd or Pb) on two different substrates - Rh(1 1 1) and Ru(0 0 0 1). The trends in miscibility for the two substrates are found to be strikingly similar. The magnetic moments show qualitatively similar behavior, but their magnitudes differ: surface alloys on Rh(1 1 1) have larger magnetic moments than on Ru(0 0 0 1). We infer that strain plays the determining role in stabilizing these two-dimensional alloys, whereas the differences in magnetic moments can be ultimately attributed to the different number of d-electrons in Rh and Ru. (C) 2009 Elsevier B. V. All rights reserved.