The structure of the γ’1 martensite in Cu-27.14 at. pct Al-3.64 at. pct Ni alloy was analyzed by the single-crystal X-ray diffraction method using various radiations. The results confirmed that the space group of the martensite was Pnmm as Kurdjumovet al.[22] reported previously, and the lattice parameters werea = 4.3896(7) A,b = 5.3424(8) A, andc = 4.2244(7) A. Using 3226 observed reflections collected with Mo Kα radiation, the atomic positional parameters were determined by the least-squares refinements (final discrepancyR factor being 6.36 pct), and the structure of the martensite was identified as a modified 2H one, with the stacking positions being deviated from the ideal positions. The site preferences of the Ni and Al atoms, which are off-stoichiometric from Cu3Al, were also determined from diffraction intensities collected with various synchrotron radiations nearK-absorption edges of Cu and Ni atoms.