THANKS TO ALMOST TWO DECADES OF OBSERVATIONS IN SOFT X-RAYS WE HAVE LEARNED A LOT ABOUT PWNE AND PULSARS POWERING THEM. MUCH.LESS IS KNOWN ABOUT THE HARD X-RAY PROPERTIES OF PWNE AND PULSARS DUE TO LIMITATIONS OF HARD X-RAY INSTRUMENTATION. THE PROPOSED.OBSERVATION OF THE FAMOUS NEARBY VELA PWN WILL FOR THE FIRST TIME RESOLVE IT IN HARD X-RAYS PROVIDING AN IMPORTANT ADDITION TO THE.SMALL SAMPLE OF PWNE OBSERVED BY NUSTAR. BOTH THE VELA PULSAR AND ITS PWN EXHIBIT UNUSUAL SPECTRAL PROPERTIES (MULTIPLE PULSED.SPECTRAL COMPONENTS VERY HARD PWN SPECTRUM) WHOSE ORIGIN MUST BE STUDIED WITH SENSITIVE OBSERVATIONS. HARD X-RAY MEASUREMENTS.ARE CRITICAL BECAUSE THEY BRIDGE THE OPTICAL/UV AND GEV DATA ON THE PULSAR AND ALLOW ONE TO LOOK FOR SYNCHROTRON COOLING AND.MAXIMUM ENERGY IN PARTICLE SED. WE WILL PERFORM PHASE-RESOLVED SPECTROSCOPY OF THE PULSAR AND COMPACT PWN WHICH WILL ALLOW US.TO DISENTANGLE THE PULSAR AND PWN COMPONENTS. WE WILL ALSO EXTRACT THE PWN SPECTRUM AWAY FROM THE PULSAR TO LOOK FOR THE EVOLUTION.OF ELECTRON SED WITH DISTANCE FROM THE PULSAR. THE OBTAINED RESULTS WILL BE CONFRONTED WITH THE PREDICTIONS OF PULSAR MAGNETOSPHERIC.EMISSION MODELS AND PULSAR WIND MODELS. THIS WORK INVOLVES DATA ANALYSIS FROM ONE OF THE NASA'S .