  We study the creep rupture of bundles of viscoelastic fibers occurring under
uniaxial constant tensile loading. A novel fiber bundle model is introduced
which combines the viscoelastic constitutive behaviour and the strain
controlled breaking of fibers. Analytical and numerical calculations showed
that above a critical external load the deformation of the system monotonically
increases in time resulting in global failure at a finite time $t_f$, while
below the critical load the deformation tends to a constant value giving rise
to an infinite lifetime. Our studies revealed that the nature of the transition
between the two regimes, i.e. the behaviour of $t_f$ at the critical load
$sigma_c$, strongly depends on the range of load sharing: for global load
sharing $t_f$ has a power law divergence at $\sigma_c$ with a universal
exponent of 0.5, however, for local load sharing the transition becomes abrupt:
at the critical load $t_f$ jumps to a finite value, analogous to second and
first order phase transitions, respectively. The acoustic response of the
bundle during creep is also studied.
