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 buildup of galaxy bulges. However, recent mid-infrared spectroscopic studies with Spitzer of a sample of bulgeless galaxies reveal 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. Detailed spectral analysis reveals that for both galaxies, the 2-10 keV emission is consistent with low-luminosity AGNs. 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 a highly absorbed X-ray source in both galaxies.