Using electroweak data and an effective Lagrangian approach we obtain stringent bounds on the tau anomalous magnetic moment, −0.004 ≤ aτ ≤ 0.006, and on its electric dipole moment, |dτ | ≤ 1.1× 10 e cm. This significantly improves our previous bounds. With the same method, we obtain limits on the dipole moments of other fermions. ∗Laboratoire associé au C.N.R.S. — URA D0063.