In supersymmetric theories the charged sleptons of different generatio
ns may oscillate amongst themselves while they decay. In the case of t
hree generation oscillations, superpartner production at the LHC and N
LC may lead to an observable CP-vioIating signal N('e(+)mu(-)) -N(mu()e(-)). This signal is proportional to a CP-violating invariant of the
slepton mass matrix, (J) over tilde, which is not constrained by sear
ches for the electric dipole moment of the electron. The sensitivity o
f the LHC and NLC to this signal is highly dependent on superpartner m
asses, but (J) over tilde may be probed to a level of 10(-3). Observat
ion of the CP-violating signal would imply a definite structure for th
e slepton mass matrices and have strong implications for models of fla
vor and SUSY breaking. (C) 1997 Elsevier Science B.V.