Context. Transit search programs such as CoRoT and Kepler now have the capability of detecting planets as small as the Earth. The detection of these planets however requires the removal of all false positives. Although many false positives can be identified by a detailed analysis of the light-curves (LCs), the detections of others require additional observations. An important source of false positives are faint eclipsing binaries within the point spread function (PSF) of the target star. For example, triple stars are an important source of false positives. Unfortunately, most of the methods previously applied have difficulties in detecting these objects. Aims: We develop a new method that allows us to detect faint eclipsing binaries with a separation smaller than one arcsec from target stars. We thereby focus on binaries that mimic the transits of terrestrial planets. These binaries can be either at the same distance as the target star (triple stars), or at either larger, or smaller distances. Methods: A close inspection of the problem indicates that these systems contain either late-type stars, or stars of high extinction. Thus, in both cases the binaries are brighter in the infrared than in the optical regime. We show how high resolution infrared (hereafter IR) spectroscopy can be used to remove these false positives. Results: For the triple star case, we find that the brightness difference between a primary and an eclipsing secondary is about 9-10 mag in the visual but only about 4.5-5.9 mag in the K-band. In the next step, we demonstrate how the triple star hypothesis can be excluded by taking a high-resolution IR spectrum. Simulations of these systems show that the companions can be detected with a false-alarm probability of ~ 2%, if the spectrum has a signal-to-noise ratio (S/N) ≥ 100. We subsequently show that high-resolution IR spectra also allows to detect most of the false positives caused by foreground or background binaries. Conclusions: If high resolution IR spectroscopy is combined with photometric methods, virtually all false positives can be detected without radial velocity (RV) measurements. It is thus possible to confirm transiting terrestrial planets with a modest investment of observing time. Partly based on observations obtained at the European Southern Observatory at Paranal, Chile in program 081.C-0033(A).