  Context. Metal-poor massive stars are supposed to be progenitors of certain
supernovae, gamma-ray bursts and compact object mergers, potentially
contributing to the early epochs of the Universe with their strong ionizing
radiation. However, they remain mainly theoretical as individual spectroscopic
observations of such objects have rarely been carried out below the metallicity
of the SMC.
  Aims. This work aims at exploring what our state-of-the-art theories of
stellar evolution combined with those of stellar atmospheres predict about a
certain type of metal-poor (0.02 Z$_{\odot}$) hot massive stars, the chemically
homogeneously evolving ones, called TWUIN stars.
  Methods. Synthetic spectra corresponding to a broad range in masses (20-130
M$_{\odot}$) and covering several evolutionary phases from the zero-age
main-sequence up to the core helium-burning stage were computed.
  Results. We find that TWUIN stars show almost no emission lines during most
of their {core hydrogen-burning} lifetimes. Most metal lines are completely
absent, including nitrogen. During their core helium-burning stage, lines
switch to emission and even some metal lines (oxygen and carbon, but still
almost no nitrogen) show up. Mass loss and clumping play a significant role in
line-formation in later evolutionary phases, particularly during core
helium-burning. Most of our spectra are classified as an early O type giant or
supergiant, and we find Wolf-Rayet stars of type WO in the core helium-burning
phase.
  Conclusions. An extremely hot, early O type star observed in a
low-metallicity galaxy could be the outcome of chemically homogeneous evolution
$-$ and therefore the progenitor of a long-duration gamma-ray burst or a type
Ic supernova. TWUIN stars may play an important role in reionizing the Universe
due to their being hot without showing prominent emission lines during the
majority of their lifetimes.
