Searches for pair-production of supersymmetric particles under the assumption of non-conservation of R-parity with a dominant LL or term have been performed using the data collected by the DELPHI experiment at LEP in e + e- collisions at centre-of-mass energies from 192 up to 208 GeV. No excess of data above Standard Model expectations was observed. The results were used to constrain the MSSM parameter space and to derive limits on the masses of supersymmetric particles.