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The chemical composition of the solar corona is not the same as that of the underlying photosphere. Elements with a first ionization potential (FIP) $\leq 10$~eV (e.g., Fe, Mg, Si, Ca) are observed to be enhanced relative to those with FIP $\geq 10$~eV (e.g., O, Ne, S) in the corona by factors of 3--10 with respect to the photosphere. This phenomenon is now commonly known as the ``FIP Effect.'' However, the reason it occurs is not known. Based on an analysis of lines from both high and low FIP species observed in Extreme Ultraviolet Explorer (EUVE) spectra, we have detected evidence for a solar-like FIP effect in the coronae of $\epsilon$~Eri (K2~V) and the $\alpha$~Cen~A and B (G2~V + K0~V) system. Conversely, our earlier analysis of Procyon (F6 IV) demonstrates that it does not exhibit a significant coronal FIP effect. The implications of these results will be discussed. Early results based on new EUVE observations of the dMe system Wolf 630 are also presented: the detection or otherwise of an FIP effect in this system has a bearing on the possible origin of galactic cosmic rays. This work has been supported by NASA contract NAS5-30180.
