The vast majority of optically identified active galactic nuclei (AGNs) in the local Universe reside in host galaxies with prominent bulges, supporting the hypothesis that black hole formation and growth is fundamentally connected to the build-up of galaxy bulges. However, recent mid-infrared spectroscopic studies with Spitzer of a sample of optically normal late-type galaxies reveal remarkably the presence of high-ionization [NeV] lines in several sources, providing strong evidence for AGNs in these galaxies. We present follow-up X-ray observations recently obtained with XMM-Newton of two such sources, the late-type optically normal galaxies NGC 3367 and NGC 4536. Both sources are detected in our observations. Detailed spectral analysis reveals that for both galaxies, the 2-10 keV emission is dominated by a power law with an X-ray luminosity in the 10^39 - 10^40 ergs s^-1 range, consistent with low luminosity AGNs. While there is a possibility that X-ray binaries account for some fraction of the observed X-ray luminosity, we argue that this fraction is negligible. These observations therefore add to the growing evidence that the fraction of late-type galaxies hosting AGNs is significantly underestimated using optical observations alone. A comparison of the mid-infrared [NeV] luminosity and the X-ray luminosities suggests the presence of an additional highly absorbed X-ray source in both galaxies, and that the black hole masses are in the range of 10^5 - 10^7 M_solar for NGC 3367 and 10^4 - 10^6 M_solar for NGC 4536.
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