We present simultaneous ASCA and RXTE observations of Ark 564, the brightest known ``narrow-line Seyfert 1 in the 2-10 keV band. The measured X-ray spectrum is dominated by a steep (Gamma~2.7) power-law continuum extending to at least 20 keV, with imprinted Fe K-line and -edge features and an additional ``soft excess below ~1.5 keV. The energy of the iron K-edge indicates the presence of highly ionised material, which we identify in terms of reflection from a strongly irradiated accretion disc. The high reflectivity of this putative disc, together with its strong intrinsic O VIII Ly-alpha and O VIII recombination emission, can also explain much of the observed soft excess flux. Furthermore, the same spectral model also provides a reasonable match to the very steep 0.1-2 keV spectrum deduced from ROSAT data. The source is much more rapidly variable than ``normal Seyfert 1s of comparable luminosity, increasing by a factor of ~50% in 1.6 hours, with no measurable lag between the 0.5-2 keV and 3-12 keV bands, consistent with much of the soft excess flux arising from reprocessing of the primary power-law component in the inner region of the accretion disc. We note, finally, that if the unusually steep power-law component is a result of Compton cooling of a disc corona by an intense soft photon flux, then the implication is that the bulk of these soft photons lie in the unobserved extreme ultraviolet.
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