****************************************************** PR # 22125 We propose 40~Ks. ASCA spectroscopic observations of the S0 galaxy NGC~4382. This galaxy is one of the early-type galaxies detected w/ the lowest X-ray to optical flux ratio, and has a peculiar X-ray spectrum, with a significant excess of counts in the lowest spectral channels, by comparison with similar {\it Einstein} & ROSAT spectra of X-ray bright E and S0 galaxies. ASCA observations will result in unprecedented high quality X-ray spectra, which will allow us to constrain the nature of the emission components and in particular to explore the possible presence of a hot ISM. With these data we will be able to constrain theoretical scenarios for the X-ray emission, and to understand how different X-ray brightness may be related to different structura ******************************************************