  We present the analysis of 200-ks NuSTAR observation of the Vela pulsar and
the pulsar wind nebula (PWN). The phase-resolved spectra corresponding to the
two main peaks in the folded pulse profile differ significantly. The spectrum
of Peak 1 is significantly harder than that of Peak 2 in qualitative agreement
with the earlier RXTE results. However, for both spectra, the best-fit values
of photon indices for the power-law (PL) fit are noticeably larger than the
previously reported values. The hardest (Peak 1) spectrum has a photon index of
$1.10\pm0.15$ which is close to those measured for the bright inner jets of the
PWN. We used the off-pulse interval to isolate pulsar emission and measure the
compact pulsar wind nebula (PWN) spectrum in hard X-rays. We also measured the
spectrum from the south-western (SW) region of the PWN which is resolved by
NuSTAR from the compact PWN. For both regions, we fit the NuSTAR spectra by
themselves and together with the Chandra X-ray Observatory spectra. We found
that the compact PWN spectrum requires a more complex model than a simple PL
with evidence for exponential cutoff in 50-80 keV. We do not find such evidence
for the spectrum extracted from the SW PWN region, located farther from the
pulsar, implying the energies over 600 TeV for the pulsar wind particles. This
may indicate in-situ particle acceleration in that region.
