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Markarian 421 and Markarian 501 are Active Galactic Nuclei and two of the most prominent sources of very high energetic gamma rays. In contrast to the predominantly stable Crab Nebula, the two blazars have extremely variable gamma-ray fluxes. Those could be caused by erratic accretion flow instabilities, but also by processes leading to quasi periodic oscillations (QPOs). Recently, hints of such a QPO of Mrk 501 with a period of about 322 days have been observed with the Large Area Telescope on-board of the Fermi satellite at GeV energies featuring global and local significances of the signal above 99%. The First G-APD Cherenkov Telescope (FACT) has monitored a small sample of known TeV gamma-ray sources including Mrk 421 and Mrk 501 over the last seven years. Therefore, it is ideally suited for periodicity studies of Active Galactic Nuclei, as they require unbiased and continuous long-term observations. Based on measurements of the well-known gamma-ray flux originating from the Crab Nebula, corrections to the measured light curves are applied. In total, 2500~hours of data for each of the two blazars have been analysed using the Lomb-Scargle algorithm. The resulting periodogram of Mrk 501 shows a hint of QPO with a similar period as the one observed by Fermi/LAT., PoS: Proceedings of Science, 358, ISSN:1824-8039, Proceedings of 36th International Cosmic Ray Conference (ICRC 2019)