Does proton stability imply the existence of an extra Z⁰?

It is well known that the minimal supersymmetric standard model admits in general Yukawa couplings violating baryon and lepton number. We argue that a generic four-dimensional SU (3) × SU (2) × U (1) string does have in general this type of dangerous couplings. We propose as the most natural solution to the proton stability problem the existence of extra low-energy gauge symmetries (U(1)'s) forbidding these terms. We construct in a systematic way the minimal extensions of the supersymmetric standard model in which gauge symmetries forbid all baryon- and/or lepton-number-violating couplings but allow Yukawa couplings for quarks and charged leptons. These models contain an extra U(1) which is not of the E₆-type.