  We propose a new class of gauge mediated supersymmetry breaking models where
the standard model gauge group is embedded into the gauge group $SU(2)_L\times
U(1)_{I_{3R}}\times U(1)_{B-L}$ [or $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$]
at the supersymmetry breaking scale $\Lambda_S$. The messenger sector in these
models can consist of color singlet but $U(1)_{I_{3R}}$ and $U(1)_{B-L}$
nonsinglet fields. The distinguishing feature of these models are (i)exact
R-parity conservation, (ii) nonvanishing neutrino masses and (iii) a unified
hidden and messenger sector potential. The simplest version of these models
predicts the existence of light gluinos which can however be made heavier by a
simple modification of the supersymmetry breaking sector.
