We use a nonperturbative QCD approach, the quark-gluon string model, to compute the τ -neutrino fluxes produced by fixed target pA collisions (where A is a target material) for incident protons of energies ranging from 120 to 800 GeV. The purpose of this calculation is to estimate in a consistent way the prompt background for the ν μ ( ν e ) ↔ ν τ oscillation search in the on-going ν μ ( ν e ) ↔ ν τ oscillation search experiments CHORUS and NOMAD, as well as the expected prompt background in future experiments, such as COSMOS at Fermilab and a possible second-generation ν μ ( ν e ) ↔ ν τ search experiment at the CERN SPS. In addition, we compute the number of ν τ interactions expected by the experiment E872 at Fermilab.