High-Velocity Clouds (HVCs) have radial velocities that cannot be explained by the global Galactic rotation; their distances remain mostly unknown, and their true nature and origin are still a mystery. Some of them could be of galactic origin, or belong to tidal streams drawn by the Milky-Way/ Magellanic Clouds interaction, or could even be intergalactic clouds infalling onto the Local Group. In the latter hypothesis, they play a major role in the hierarchical formation scenario of the Milky-Way and are connected to the Lyman-limit absorption systems. In any case, the determination of their physical state (density, temperature, internal structure, abundances, excitation) will help to discriminate between current theories on their origin and nature. A recent UV measurement (Richter et al 1999) has discovered for the first time in a HVC the molecular phase that was previously searched for, without success, through CO emission. Previous non detections could be due either to metallicity problems, or insufficient excitation (because of low density). Low-excitation molecular gas may, however, be detectable though absorption. Here we report on a sensitive search for HCO+(1-0) absorption lines in front of 27 quasars, already known to be strong millimetric continuum sources. Except for one tentative case, no detection was obtained in most HVCs, although HCO+(1-0) was clearly detected towards galactic low-velocity clouds. We discuss the implications of this result.
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