  We review the reports of possible year-long quasi-periodicities of BL Lac
objects in the $\gamma$-ray and optical bands, and present a homogeneous time
analysis of the light curves of PKS2155$-$304, PG1553+113, and BL Lac. Based on
results from a survey covering the entire Fermi $\gamma$-ray sky we have
estimated the fraction of possible quasi-periodic BL Lac objects. We compared
the cyclical behaviour in BL Lac objects with that derived from the search of
possible optical periodicities in quasars, and find that at z$\lesssim$1 the
cosmic density of quasi-periodic BL Lac objects is larger than that of
quasi-periodic quasars. If the BL Lac quasi-periodicities were due to a
supermassive binary black hole (SBBH) scenario, there could be a tension with
the upper limits on the gravitational wave background measured by the pulsar
timing array. The argument clearly indicates the difficulties of generally
associating quasi-periodicities of BL Lac objects with SBBHs.
