High-resolution spectroscopic observations of the local interstellar medium between the Sun and nearby stars have been recorded with the Aurelie spectrometer of the Observatoire de Haute Provence (France). They have been used to identify and characterize the local interstellar cloud (LIC) in which the Sun is embedded. The ''Doppler triangulation'' shows that the local cloud flows toward &lgr;=74.9¿; &bgr;=-7.8¿ at a velocity of 25.7¿1.0 kms-1 with respect to the Sun. This is strongly confirmed by Hubble space telescope (HST) UV measurements toward the star Capella. Furthermore, the recent detection of interstellar neutral helium inside the heliosphere, found to flow at 26.0¿1.0 kms-1 with the Ulysses Neutral Gas Experiment, brings a definitive proof of this identification. The common interval for the local cloud temperature from these three different types of measurements is 7000¿200 K. As a consequence of the LIC velocity determination, the interstellar neutral hydrogen found to flow at 20 kms-1 through the solar system is shown to be decelerated by 6 kms-1 and slightly heated up to 8000 K due to coupling with the plasma at the heliospheric interface. Further high-resolution spectroscopic observations with the HST-Goddard high-resolution spectrometer (provided the short wavelength part can be repaired) should supply the local interstellar electronic density. These informations are of crucial importance with respect to the understanding of the heliospheric cavity. ¿ American Geophysical Union 1993