****************************************************** PR # 11068 With the Ginga satellite, we found that shell-like supernova remnants (SNRs)have hard X-ray tails in addition to the soft (typically below 1 keV) thermal components. The most clear example of the hard X-ray emission was found in IC443 and HB9. To search for the origin of the hard Xray emission,we propose the observation of these two SNRs IC443 and HB9. These observations are also important for the study of SNRs which are interacting with molecular clouds. Using ASCA, we can get a temperature and distribution across the remnants,and find the distrib ution of the hard X-ray components for the first time. With high qual ity X-ray spectra from several positions of the SNRs and comparison with the spatial distribution of the molecular cloud, we can address the origin of hard X-ray emiss ******************************************************