************************************************************************* 63031 The ROSAT All Sky Survey revealed a number of IRAS galaxies with high X-ray luminosities. Generally they have steep soft X-ray spectra and are not classified unambiguosly as active or non-active galaxies. It is proposed to expand on an earlier observation by studying two further cases with ASCA, so as to establish the nature of these objects and determine the relative importance of Starburst and AGN processes in producing the high emission levels. An AGN component may show up at harder X-rays, while the contribution of thermal emission associated with Starburst can be established from the soft part of the ASCA X-ray spectrum. The results of this study are of great interest in view of competing explanations with AGN or with Starburst for low activity levels in otherwise normal galaxies. *************************************************************************