  We have investigated the possible existence of a quasi-bound state for the
\Sigma -\Sigma -\alpha system in the framework of Faddeev calculations. We are
particularly interested in the state of total iso-spin T=2, since for an inert
\alpha particle there is no strong conversion to \Xi -N-\alpha or \Lambda
-\Lambda -\alpha possible. A \Sigma -\alpha optical potential based on Nijmegen
model D and original \Sigma -\Sigma interactions of the series of Nijmegen
potentials NSC97 as well a simulated Gaussian type versions thereof are used.
Our investigation of the \Sigma -\Sigma -\alpha system leads to a quasi bound
state where, depending on the potential parameters, the energy ranges between
-1.4 and -2.4 MeV and the level width is about 0.2MeV.
