Pure and high-quality single-crystal Nb(001) thin films with thicknesses ranging from 40 AA to 1000 AA were grown epitaxially on NaCl(001) substrates by an UHV E-beam evaporation technique. TEM observations, resistivity and superconducting transition temperature measurements were carried out. A drastic fall-off in transition temperature and conductivity was observed in ultrathin single-crystal Nb films. The results are discussed within the framework of the existing theories and a strain-induced 'double-layer' model is proposed. Data for polycrystalline Nb thin films on glass substrates deposited under exactly the same evaporation conditions as the single-crystal films are also presented for comparison.