SUSY model with R-parity violation, longlived charged slepton and   quasistable matter
  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. 
N.V.Krasnikov