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We present the ASCA observation of several flare events on Proxima Centauri during March 18-20 1994. Although the quiescent count rate of 0.23 cts/sec was too low to unambiguously spot line features, flares were clearly distinguished with a higher count rate of approximately 0.9 cts/sec. These are the first stellar flares observed to overlap with ordinary solar flares of class M on the GOES scale (Haisch, Antunes and Schmitt, 1995, Science, in press). We compared the quiescent data with the flare data, and fit the X-ray emission using two-temperature and differential emission measure plasma models. Unlike several coronal sources (for example, Algol, AR Lac), the models did not require sub-solar abundances. However, abundance determinations in the absence of clearly distinguishable lines were uncertain. The current results support the premise that the coronal X-ray emission is a result of the superposition of many flares.