************************************************************************* 61101 We propose observations of X-ray unbiased sample of LINERs in nearby galaxies. About 10 LINERs have been observed by ASCA to search for AGNs. Low luminosity AGN, X-ray luminosity ranging from 10E40 to 10E41 erg/s, are found in most of them. However they are biased to those galaxies which exhibit AGN like activities in various form. We selected 2 LINER galaxies with large Halpha flux to construct an Halpha limited sample. Our aims are (1)to understand physics in LINERs using a well selected small sample, (2)to calibrate correlations between X-ray and other wavelength properties (3)to estimate the X-ray luminosity function of AGN at the low luminosity end and to set limits to contribution to the X-ray background using optical complete survey results and X-ray results. *************************************************************************