A study of events containing two tau leptons with high transverse momentum has been performed with the ZEUS detector at HERA, using a data sample corresponding to an integrated luminosity of 0.33 fb-1. The tau candidates were identified from their decays into electrons, muons or hadronic jets. The number of tau-pair candidates has been compared with the prediction from the Standard Model, where the largest contribution is expected from Bethe-Heitler processes. The total visible cross section was extracted. Standard Model expectations agree well with the measured distributions, also at high invariant mass of the tau pair.