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A search for tau neutrino induced showers with the MAGIC telescopes ispresented. The MAGIC telescopes located at an altitude of 2200 m a.s.l. in theCanary Island of La Palma, can point towards the horizon or a few degrees belowacross an azimuthal range of about 80 degrees. This provides a possibility tosearch for air showers induced by tau leptons arising from interactions of tauneutrinos in the Earth crust or the surrounding ocean. In this paper we showhow such air showers can be discriminated from the background of very inclinedhadronic showers by using Monte Carlo simulations. Taking into account theorography of the site, the point source acceptance and the event rates expectedhave been calculated for a sample of generic neutrino fluxes fromphoto-hadronic interactions in AGNs. The analysis of about 30 hours of datataken towards the sealeads to a 90\% C.L. point source limit for tau neutrinosin the energy range from $1.0 \times 10^{15}$ eV to $3.0 \times 10^{18}$ eV ofabout $E_{\nu_{\tau}}^{2}\times \phi (E_{\nu_{\tau}}) < 2.0 \times 10^{-4}$ GeVcm$^{-2}$ s$^{-1}$ for an assumed power-law neutrino spectrum with spectralindex $\gamma$=-2. However, with 300 hours and in case of an optimisticneutrino flare model, limits of the level down to $E_{\nu_{\tau}}^{2}\times\phi (E_{\nu_{\tau}}) < 8.4 \times 10^{-6}$ GeV cm$^{-2}$ s$^{-1}$ can beexpected.

Limits on the flux of tau neutrinos from 1 PeV to 3 EeV with the MAGIC telescopes