  We investigate the formation by accretion of massive primordial protostars in
the range 10 to 300 Msun. The high accretion rate used in the models (4.4 x
10^{-3} Msun/yr) causes the structure and evolution to differ significantly
from those of both present-day protostars and primordial zero-age main sequence
stars. After an initial expansion of the radius (for < 12 Msun), the protostar
undergoes an extended phase of contraction (up to 60 Msun). The stellar surface
is not visible throughout most of the main accretion phase, since a photosphere
is formed in the infalling envelope. Also, significant nuclear burning does not
take place until a protostellar mass of about 80 Msun. As the interior
luminosity approaches the Eddington luminosity, the protostellar radius rapidly
expands, reaching a maximum around 100 Msun. Changes in the ionization of the
surface layers induce a secondary phase of contraction, followed by a final
swelling due to radiation pressure when the stellar mass reaches about 300
Msun. This expansion is likely to signal the end of the main accretion phase,
thus setting an upper limit to the protostellar mass formed in these
conditions.
