************************************************************************* 51035 ASCA has observed only one red giant star altough ROSAT has been detecting some red, red bright and red super giant stars. However, Due to the poor energy resolution of ROSAT observatory, temperature, abundance and absorption column of X-rays from these evolved late-type stars are still unknown. Hence, no clear observational ansower to the emission and the heating mechanism has been obtained. This is the first attempt to obatin precise X-ray spectra of these stars and give a clear observational ansower to the questions. *************************************************************************