Proton Stability and Small Neutrino Mass in String Inspired $E_6$ Models

We propose a new possibility to realize simultaneously the sufficient proton stability and the interesting structure of neutrino mass matrix in superstring inspired $E_6$ models. In this model the leptons and Higgs fields are assigned to a fundamental representation {\bf 27} in the different way among generations. Two pairs of Higgs doublets naturally remain light from three generation ones by imposing certain discrete symmetries, although all extra color triplets become sufficiently heavy. Under these symmetries suitable $\mu$-terms to bring appropriate vacuum expectation values are prepared and the dangerous FCNC is avoidable. Some related phenomena to this model, especially, the structure of neutrino mass matrix are also discussed.