Electron-capture spectroscopy has been used to investigate long-ranged and short-ranged two-dimensional magnetic order at free (uncoated) surfaces of homogeneous (island-free), ultrathin fcc γ-Fe(111)(1×1) films pseudomorphically deposited on Cu(111) substrate crystals. At 298 K, the electron-spin polarization at the surface of a four-monolayer thin fcc Fe film amounts to +16%, directly revealing the existence of long-ranged ferromagnetic order. There is evidence that short-ranged ferromagnetic order still exists at 400 K at free surfaces of two and one-monolayer thin fcc Fe films.