  We present a phenomenological study of tau-sleptons stau_1,2 and
tau-sneutrino in the Minimal Supersymmetric Standard Model with complex
parameters A_tau, mu and M_1. We analyse production and decays of stau_1,2 and
tau-sneutrino at a future e^+ e^- collider. We present numerical predictions
for the important decay rates, paying particular attention to their dependence
on the complex parameters. The branching ratios of the fermionic decays of
stau_1 and tau-sneutrino show a significant phase dependence for tan(beta) <
10. For tan(beta) > 10 the branching ratios for the stau_2 decays into Higgs
bosons depend very sensitively on the phases. We show how information on the
phase phi(A_tau) and the other fundamental stau parameters can be obtained from
measurements of the stau masses, polarized cross sections and bosonic and
fermionic decay branching ratios, for small and large tan(beta) values. We
estimate the expected errors for these parameters. Given favorable conditions,
the error of A_tau is about 10% to 20%, while the errors of the remaining stau
parameters are in the range of approximately 1% to 3%. We also show that the
induced electric dipole moment of the tau-lepton is well below the current
experimental limit.
