  We illustrate the sensitivities of LEP experiments to leptonic signals
associated to models where supersymmetry (SUSY) is realized with spontaneous
breaking of R-parity. We focus on missing transverse momentum plus acoplanar
muon events arising from lightest neutralino single production $\chi \nu$ as
well as pair production $\chi \chi$, followed by $\chi$ decays, where $\chi$
denotes the lightest neutralino. We show that the integrated luminosity
achieved at LEP already starts probing the basic parameters of the theory. We
discuss the significance of these constraints for the simplest spontaneous
R-parity breaking models and their relevance for future searches of SUSY
particles.
