****************************************************** PR # 32022 Contrary to the evidence suggested by Einstein and EXOSAT data, very low-mass stars at the bottom of the main-sequence do have coronae. These stars have completely convective structures and are slowly rotating. The origin and energetics of their coronae are not presently understood. ROSAT recently measured the broadband X-ray flux for only 8 of these stars, most of which are too faint and either are close binaries or have nearby companions. CN Leo (dM6e, $<$0.10 solar mass) provides the best opportunity to measure the quiescent coronal spectrum with ASCA. Although a flare star, it is relatively inactive, enabling its quiescent state to be measured. The differential emission measure will be determined, and variability searched for in the quiescent ******************************************************