Supersymmetric theories generally have new flavor violation sources in the squark and slepton mass matrices. If significant lepton flavor violation exists, selectron and smuon should be nearly degenerate. This leads to the phenomenon of slepton oscillations, which is analogous to neutrino oscillations, if sleptons are produced at the Next Linear Collider. The direct slepton production at the Next Linear Collider provides a much more powerful probe of lepton flavor violation than the current bounds from rare processes, such as (mu) (r arrow) e(gamma). 4 refs., 1 fig.