We present a combined in situ surface stress and structural study of MnCu surface alloys formed by deposition of Mn on Cu(001) at 300 and 420 K. Mn-induced surface alloying induces a compressive stress change, which grows in proportion to the Mn coverage up to 0.5 monolayers (ML), where it reaches –1.2 N/m (1 ML: 1.5x10¹⁵ atoms cm⁻²). This stress is related to the formation of the c(2x2) surface alloy. No further alloying is observed upon subsequent Mn deposition at 300 K, at 420 K the formation of the p2gg(4x2) Mn-Cu alloy occurs, and a compressive stress change of –2.3 N/m at 1.3 ML is found. Surface x-ray-diffraction analysis of the two-layer alloy p2gg(4x2)-phase indicates an amplitude of 0.9 Å for vertical buckling and lateral modulations of the atomic positions, the latter leading to the doubling of the lattice constant as compared to the c(2x2) structure. Evidence for a compositional gradient within the alloy structure is given, where the Mn concentration is above and below 50% in the topmost and second alloy layer, respectively. The importance of surface stress relief and Mn/Cu atomic size mismatch for the Mn-induced surface stress change is discussed.