  High-energy radiation of young pulsar wind nebulae (PWNe) is known to be
variable. This is most prominently exemplified by the Crab nebula which can
undergo both rapid brightenings and dimmings. Two pulsars in the Large
Magellanic Cloud, PSR J0540-6919 and PSR J0537-6910 are evolutionally very
close to Crab, so one may expect the same kind of variability from the PWNe
around them as from the Crab nebula. In this work we search for variability in
these PWNe in gamma rays using the data from the Fermi Large Area Telescope in
the range 100 MeV-10 GeV collected from August 2008 to December 2021. We
construct light curves of these sources in the three bands, 100-300 MeV,
300-1000 MeV and 1-10 GeV with the one week time resolution. We find evidence
of flaring activity in all the bands, in contrast with Crab, where no flares at
$E>1$ GeV were observed. Analysis of the flaring episode in the 100-300 and
300-1000 MeV bands indicates that the flux of one of the PWNe could grew by a
factor of $\approx 5-10$. We are not confident about which of the two PWNe
flared because of their proximity in the sky. However, in the 1-10 GeV band
where the angular resolution of the LAT is better, we find several episodes of
enhanced brightness in both the PWNe. We check possible contaminants which
could be responsible for the observed variability, but find their contribution
not to be relevant.
