  We study the evolution of the first stars in the universe (Population III)
from the early pre-Main Sequence until the end of helium burning in the
presence of WIMP dark matter annihilation inside the stellar structure. The two
different mechanisms that can provide this energy source are the contemporary
contraction of baryons and dark matter, and the capture of WIMPs by scattering
off the gas with subsequent accumulation inside the star. We find that the
first mechanism can generate an equilibrium phase, previously known as a "dark
star", which is transient and present in the very early stages of pre-MS
evolution. The mechanism of scattering and capture acts later, and can support
the star virtually forever, depending on environmental characteristic of the
dark matter halo and on the specific WIMP model.
