  The temporal dynamics of double ionization of H2 has been investigated both
experimentally and theoretically with few-cycle laser pulses. The main
observables are the proton spectra associated to the H^+ + H^+ fragmentation
channel. The model is based on the time-dependent Schr\"odinger equation and
treats on the same level the electronic and nuclear coordinates. Therefore it
allows to follow the ultrafast nuclear dynamics as a function of the laser
pulse duration, carrier-envelope phase offset and peak intensity. We mainly
report results in the sequential double ionization regime above 2 10^{14}
W/cm^2. The proton spectra are shifted to higher energies as the pulse duration
is reduced from 40fs down to 10fs. The good agreement between the model
predictions and the experimental data at 10fs permits a theoretical study with
pulse durations down to a few femtoseconds. We demonstrate the very fast
nuclear dynamics of the H2^+ ion for a pulse duration as short as 1fs between
the two ionization events giving respectively H2^+ from H2 and H^+ + H^+ from
H2^+. Carrier-envelope phase offset only plays a significant role for pulse
durations shorter than 4fs. At 10fs, the laser intensity dependence of the
proton spectra is fairly well reproduced by the model.
