  M82 X-2 is the first pulsating ultraluminous X-ray source (PULX)to be
identified. Since the discovery in 2014, NuSTAR has observed the M82 field 15
times throughout 2015 and 2016. In this paper, we report the results of
pulsation searches in all these datasets, and find only one new detection. This
new detection allows us to refine the orbital period of the source and measure
an average spin down rate between 2014 and 2016 of 5x10^-11 Hz/s, which is in
contrast to the strong spin up seen during the 2014 observations and represent
the first detection of spin down in a PULX system. Thanks to the improved
orbital solution allowed by this new detection, we are also able to detect
pulsations in additional segments of the original 2014 dataset. We find a
glitch superimposed on the very strong and variable spin-up already reported,
the first positive glitch identified in a PULX system. We discuss the new
findings in the context of current leading models for PULXs.
