************************************************************************* 51123 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 10^40 to 10^41 erg/s, were found from most of them. However they are biased to those galaxies which exhibit AGN like activities such as broad H-alpha, jet, compact radio core, point-like X-ray source in Einstein images and so on. We selected 3 galaxies with large narrow Halpha flux. Our aim is (1)to understand physics in LINERs using well selected small samples, (2)to calibrate X-ray and other wavelength properties (3)to estimate X- ray luminosity function of AGN at low luminosity end and to set limits to contribution to The X-ray background using optical complete survey results and X-ray results. *************************************************************************