************************************************************************* 71086 Super Luminous Point Sources (SLPS) which is considered to be a single point source but have an X-ray luminosity of 10^{39} to 10^{40} erg/sec are found at off-center positions of about twenty nearby spiral galaxies. Some SLPSs were found near the center of the galaxy but not in the nucleus. These sources still remain as one of the most mysterious classes of objects, even after extensive studies with Einstein, ROSAT, and ASCA. In particular ASCA observations revealed the X-ray spectra and temporal variations of many of this class of objects. For the further study of these class of objects, we propose to observe one nearby spiral galaxies, NGC 4559 and, which contain two SLPS,one is near the center and another is offset about 2' from the center. *************************************************************************