The production and decay of τ-pairs was studied with the JADE detector at PETRA at center-of-mass energies of 30 ⩽√s ⩽ 46.78 GeV. The total production cross section for τ-pairs agreed with QED predictions to order α3. Lower limits on QED cut-off parameters of Λ+ > 285 GeV and Λ− > 210 GeV at 95% confidence level were ontained. The decay branching fractions into one and three charged particles were determined to be (86.1 ± 0.5 ± 0.9)% and (13.6±0.5 ±0.80)%. In the angular distributions a forward-backward asymmetry was observed, from which the axial-vector weak charge to the τ was determined to be aτ = −0.74 ± 0.22 in agreement with the standard model. An analysis of the process e+e− → τ+τ−γ showed agreement with QED calculations to O(α3).