  If the scalar tau $\stau$ is the next lightest supersymmetric particle and
decays into a gravitino ($\gravitino$) being the lightest supersymmetric
particle, it will have generally a very long lifetime. In this paper, we
investigate the possibility to study the decay of such a long lived scalar tau
at the LHC. If we can add to the present LHC experiments additional detectors
which are able to stop the stau particles and measure the produced decay
products, the decay characteristics can be studied precisely at the LHC. We
identify a maximum "stopper detector" that could be added in the CMS cavern,
and estimate the sensitivity to the lifetime of the stau and to the mass of
gravitino with this detector. The decay of the scalar tau may be significantly
modified if the decay channel to the axino $\axino$ is open. We study the
possibility to distinguish such decays from decays into gravitinos by measuring
the process $\stau\to \axino (\gravitino) \tau \gamma$ using the stopper
detector.
