  We present spectral and timing analysis of NuSTAR observations of the
accreting X-ray pulsar 2RXP J130159.6-635806. The source was serendipitously
observed during a campaign focused on the gamma-ray binary PSR B1259-63 and was
later targeted for a dedicated observation. The spectrum has a typical shape
for accreting X-ray pulsars, consisting of a simple power law with an
exponential cutoff starting at ~7 keV with a folding energy of E_fold=~18 keV.
There is also an indication of the presence of a 6.4 keV iron line in the
spectrum at the ~3 sigma significance level. NuSTAR measurements of the
pulsation period reveal that the pulsar has undergone a strong and steady
spin-up for the last 20 years. The pulsed fraction is estimated to be ~80%, and
is constant with energy up to 40 keV. The power density spectrum shows a break
towards higher frequencies relative to the current spin period. This, together
with steady persistent luminosity, points to a long-term mass accretion rate
high enough to bring the pulsar out of spin equilibrium.
