Metal-poor massive stars are assumed to be progenitors of certain supernovae, gamma-ray bursts, and compact object mergers that might contribute to the early epochs of the Universe with their strong ionizing radiation. However, this assumption remains mainly theoretical because individual spectroscopic observations of such objects have rarely been carried out below the metallicity of the Small Magellanic Cloud. Aims. Here we explore the predictions of the state-of-the-art theories of stellar evolution combined with those of stellar atmospheres about a certain type of metal-poor (0.02 Z·) hot massive stars, the chemically homogeneously evolving stars that we call Transparent Wind Ultraviolet INtense (TWUIN) stars. Methods. We computed synthe...