Searches for supersymmetric particles produced in e(+)e(-) interactions at the Z peak have been performed under the assumptions that R-parity is not conserved, that the dominant R-parity violating coupling involves only leptonic fields, and that the lifetime of the lightest supersymmetric particle can be neglected. In a data sample collected by the ALEPH detector at LEP up to 1993, and corresponding to almost two million hadronic Z decays, no signal was observed. As a result, supersymmetric particle masses and couplings are at least as well constrained as under the usual assumption of R-parity conservation.