****************************************************** PR # 32229 We propose to use the ASCA SIS to study the ubiquitous oxygen absorption feature at unprecedented spectral resolution in Mrk 501. We will also search for carbon K edge absorption, of which the SIS should be capable of detecting if the ionization state is CIII or higher. This will enable us to distinguish ``warm'' (O IV + C IV) an d ``hot'' (O VI + C VI) absorbing scenarios. Mrk 501 is favorable, g iven its low $N_H$, low $z$, and lack of cluster contamination, in c omparison to other BL Lacs studied with the SIS. Indeed, a direct c omparison with Mrk 521 (which has simlilar variability properties) s hould be undertaken. We will donate our data to help determine an i n-flight calibration for the SIS1 detector (which was apparently notc alibrated below 1 keV on the g ******************************************************