  Relic thermal axions could play the role of an extra hot dark matter
component in cosmological structure formation theories. By combining the most
recent observational data we improve previous cosmological bounds on the axion
mass m_a in the so-called hadronic axion window. We obtain a limit on the axion
mass m_a < 0.42eV at the 95% c.l. (m_a < 0.72eV at the 99% c.l.). A novel
aspect of the analysis presented here is the inclusion of massive neutrinos and
how they may affect the bound on the axion mass. If neutrino masses belong to
an inverted hierarchy scheme, for example, the above constraint is improved to
m_a < 0.38eV at the 95% c.l. (m_a < 0.67eV at the 99% c.l.). Future data from
experiments as CAST will provide a direct test of the cosmological bound.
