Two series of epitaxial Ni-Mn-Sn thin films of different thickness are investigated for the thickness and composition dependence of the martensitic transformation. Thin films ranging in thickness from 20 to 200 nm (series A) and 10 to 100 nm (series B) were prepared by magnetron co-sputtering and deposited on heated MgO(001) substrates. The structural characterization was done by temperature-dependent X-ray diffraction measurements. Magnetization and resistivity measurements were performed to investigate the transformation characteristics. We find a strong influence of the film thickness on the relative amount of material undergoing the martensitic transformation, the temperature range of the transformation, and the transformation temperatures. The main contribution originates from the rigid substrate which delays the transformation of the Ni-Mn-Sn near the interface and even leads to a layer of residual austenite at low temperatures. Another issue are size effects which presumably broaden the martensitic transformation and decrease the transformation temperatures. By variation of the thin film composition we find changes of the substrate influence due to a different mismatch between the lattice of MgO and austenite. A better phase compatibility between martensite and austenite, denoted by lambda(2), not only results in a smaller hysteresis but is also beneficial for the transformation of material close to the substrate. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.