I will present periodicity search results on the gamma-ray lightcurve of the TeV blazar PKS 1510- 089, observed by the Fermi Large Area Telescope. Our analyses detected two transient quasi-periodic oscillations (QPOs): a 3.6-day QPO during the outburst in 2009 that lasted five cycles (MJD 54906–54923); and a periodicity of 92 days spanning over 650 days from 2018 to 2020 (MJD 58200–58850), which lasted for seven cycles. We employed the Lomb-Scargle periodogram, Weighted Wavelet Z-transform, REDFIT, and Monte Carlo lightcurve simulation techniques to find any periodicity and the corresponding significance. The 3.6-day QPO was detected at a moderate significance of ~3.5σ, while the detection significance of the 92-day QPO was ~7.0σ. We also applied the same QPO search methods on the longterm optical R-band lightcurve of another blazar AO 0235+164, and detected a persistent QPO of 8.13 years with ~6.0σ. We explore a few physical models for such QPOs of various timescales including a binary black hole system, the precession of the jet, a non-axisymmetric instability rotating around the central black hole near the innermost stable circular orbit, the presence of quasi-equidistant magnetic islands inside the jet, and a geometric model involving a plasma blob moving helically inside a curved jet. Furthermore, I will present a few more results on long-term and intraday variability study of multi-waveband optical lightcurves of blazar AO 0235+164.
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