  We construct SUSY $SU(3) \otimes SU(2)_{L} \otimes U(1)$ electroweak models
with superweak R-parity. The scale of R-parity violation in one of the models
is determined by the Majorana mass of neutrino and it is very small that leads
to the existence of longlived ($ T \geq O(10^{-4}sec$) lightest superparticle.
If lightest superparticle is righthanded charged slepton that can be realized
within gaugino dominated scenario then the phenomenology of such model differs
in a drastic way from the standard SUSY phenomenology, in particular, longlived
charged sleptons can form bound states with ordinary matter - quasistable
supermatter (SUSY analogs of mu-atoms and muonium). We discuss possible
manifestations of the existence of such longlived charged particle at LEP2,
TEVATRON and LHC. We also construct $SU(3) \otimes SU(2)_{L} \otimes SU(2)_{R}
\otimes U(1)$ model with Majorana mass and superweak R-parity violation.
