  GS 0836-429 is a neutron star X-ray transient that displays Type-I X-ray
bursts. In 2003 and 2004 it experienced two outbursts in X-rays. We present
here an analysis of the system bursting properties during these outbursts. We
studied the evolution of the 2003-2004 outbursts in soft X-rays using RXTE
(2.5-12 keV; ASM), and in hard X-rays with INTEGRAL (17-80 keV, IBIS/ISGRI).
Using data from the JEM-X monitor onboard INTEGRAL we detected 61 Type-I X-ray
bursts, and confirm that the source displayed a quasi-periodic burst recurrence
time of about 2.3 hours. We improve the characterization of the fuel
composition, as well as the description of the typical burst durations and
fluences. We estimate the average value of $\alpha$ to be $49\pm\,3$. This
value together with the observed burst profiles indicate a regime of a mixed
He/H runaway triggered by unstable helium ignition. In addition, we report the
detection of four series of double bursts, with burst recurrence times of
$\leq\,20$ minutes. The measured recurrence time in double bursts is too short
to allow the accretion of enough fresh material, necessary to trigger a Type-I
X-ray burst. This suggests the presence of left-over, unburned material from
the preceding burst which gets ignited in a time scale of minutes. The energies
and time scales of the secondary bursts suggest a lower fraction of hydrogen
compared to that estimated for the primary bursts. The persistent emission was
roughly constant during the period when the Type I X-ray bursts were detected.
We derive an average accretion rate during our observations of
$\dot{m}\sim\,8\,\%\,\dot{m}_{Edd}$. The spectrum of the persistent emission
can be fit with a non-thermal component, indicative for the source to be in a
hard state when the INTEGRAL observations were performed.
