Searches for spontaneous R-parity violating signals at sqrt(s) = 183 GeV and sqrt(s) = 189 GeV have been performed using the 1997 and 1998 DELPHI data, under the assumption of R-parity breaking in the third lepton family. The expected topology for the decay of a pair of charginos into two acoplanar taus plus missing energy was investigated and no evidence for a signal was found. The results were used to derive a limit on the chargino mass and to constrain the allowed domains of the MSSM parameter space.