Our goal in this paper is to examine the discovery potential of labora
tory experiments searching for the oscillation nu(mu)(nu(e)) --> nu(ta
u), in the light of recent data on solar and atmospheric neutrino expe
riments, which we analyse together with the most restrictive results f
rom laboratory experiments on neutrino oscillations. In order to expla
in simultaneously all present results we use a four-neutrino framework
, with an additional sterile neutrino. Our predictions are rather pess
imistic for the upcoming experiments NOMAD and CHORUS, which, we find,
are able to explore only a small area of the oscillation parameter sp
ace. On the other hand, the discovery potential of future experiments
is much larger. We consider three examples. E803, which is approved to
operate in the future Fermilab main injector beam line, MINOS, a prop
osed long-baseline experiment also using the Fermilab beam, and NAUSIC
AA, an improved detector which improves by an order of magnitude the p
erformance of CHORUS/NOMAD and can be operated either at CERN or at Fe
rmilab beams. We find that those experiments can cover a very substant
ial fraction of the oscillation parameter space, having thus a very go
od chance of discovering both nu(mu) --> nu(tau) and nu(e) --> nu(tau)
oscillation modes.