  We examine the effects of the lepton number violating R parity odd
interactions, $\lambda_{ijk} $, on single production of fermion (charginos and
neutralinos) and scalar (sleptons and sneutrinos) superpartners at leptonic
colliders for center of mass energies up to $500GeV - 1TeV$. The probability
amplitudes for all the five relevant $2 \to 2$ body processes and the decays
branching ratios for the produced superpartners are calculated at tree level. A
semi-quantitative discussion is developed within a supergravity model assuming
grand unification of gauge interactions and universal (flavor independent) soft
supersymmetry breaking parameters at the unification scale. The predictions
obtained for the total and partial rates show that the single production
reactions have a good potential of observability at NLC (Next Linear Colliders)
energies. For values of the R parity violating coupling constant, $\lambda
_{ijk}= 0.05$, close to the current bounds, the $\tilde \chi^{\pm, 0}$
reactions could probe all the relevant intervals for $\tan \beta$ and $m_0$ and
broad regions of the parameter space for $\mu$ and $M_2$, while the $\tilde \nu
$ and $\tilde l $ productions could probe sneutrinos and sleptons masses up to
the kinematical limits. Using the hypothesis of a single dominant R parity
violating coupling constant, a Monte Carlo events simulation for the $ \tilde
\chi^{\pm, 0} $ reactions is employed to deduce some characteristic final
states dynamical distributions.
