  The capability of generating two intense, femtosecond x-ray pulses with
controlled time delay opens the possibility of performing time-resolved
experiments for x-ray induced phenomena. We have applied this capability to
study the photoinduced dynamics in diatomic molecules. In molecules composed of
low-Z elements, \textit{K}-shell ionization creates a core-hole state in which
the main decay mode is an Auger process involving two electrons in the valence
shell. After Auger decay, the nuclear wavepackets of the transient
two-valence-hole states continue evolving on the femtosecond timescale, leading
either to separated atomic ions or long-lived quasi-bound states. By using an
x-ray pump and an x-ray probe pulse tuned above the \textit{K}-shell ionization
threshold of the nitrogen molecule, we are able to observe ion dissociation in
progress by measuring the time-dependent kinetic energy releases of different
breakup channels. We simulated the measurements on N$_2$ with a molecular
dynamics model that accounts for \textit{K}-shell ionization, Auger decay, and
the time evolution of the nuclear wavepackets. In addition to explaining the
time-dependent feature in the measured kinetic energy release distributions
from the dissociative states, the simulation also reveals the contributions of
quasi-bound states.
