LEAR 60 CREW GOES OFF COURSE ON THE BOACH DEP DEPARTING LAS.

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WE TOOK OFF FROM LAS ON RWY 19R AT XA43Z. THE FO WAS THE PF AND THE CLRNC WAS TO FLY THE BOACH TWO RNAV DEP. THE FO WAS HAND FLYING THE ACFT ON THE RNAV DEP USING THE FLT DIRECTOR. AS THIS WAS A POS LEG WITHOUT PAX HE WAS CLBING AT A RAPID RATE OF APPROX 4000-6000 FPM. AFTER I COMPLETED THE AFTER TKOF CHKLIST I NOTICED THAT WE APPEARED TO BE SLIGHTLY OFF COURSE. I MENTIONED THIS TO THE FO AND HE BEGAN TO CORRECT TOWARD THE PROPER COURSE. WE WERE BOTH PUZZLED AS TO THE REASON FOR THE COURSE DEV BECAUSE THE RNAV DEP WAS CORRECTLY DISPLAYED ON BOTH OUR PFD'S. BEFORE WE WERE ABLE TO CONTINUE ANALYZING THE CIRCUMSTANCES BEHIND OUR DEV THE DEP CTLR CALLED AND SAID THAT WE WERE NOT ON THE RNAV DEP. I STATED THAT WE HAD GONE OFF THE COURSE BUT THAT WE WERE CORRECTING TO GET BACK ON IT. THE CTLR THEN GAVE US DIRECTIONS TO FLY OUR PRESENT HDG TO INTERCEPT AND TRACK INBOUND ON THE 213 DEG RADIAL TO HEC. WE WERE THEN IMMEDIATELY PASSED ON TO ANOTHER FREQ. DUE TO THE NEW CLRNC AND ITS ASSOCIATED WORKLOAD ALONG WITH THE RAPID HDOF WE WERE UNABLE TO DETERMINE THE EXACT REASON FOR OUR DEV. I BELIEVE THIS ALL OCCURRED BTWN THE ROPPR-RODDD FIXES ON THE DEP. I ESTIMATE WE STRAYED OFF COURSE 2-4 NM. POSSIBLE CAUSES/CONTRIBUTING FACTORS: 1) AUTOPLT/FLT DIRECTOR MALFUNCTION -- LATER IN THE FLT WHILE ON DSCNT WITH THE AUTOPLT FLYING WE INEXPLICABLY BEGAN TO CLB. AS WE WERE ALERT TO THE POSSIBILITY OF AN AUTOPLT PROB EARLIER WE WERE BOTH CLOSELY MONITORING OUR FLT PATH AND THE FO IMMEDIATELY BEGAN HAND FLYING THE ACFT. AFTER DSCNT WAS AGAIN STABILIZED THE AUTOPLT WAS ENGAGED AND NO OTHER PROBS WERE NOTED. 2) LEAR 60 FLT DIRECTOR OP -- BECAUSE OUR LR60 NORMALLY OPERATES WITH A 'SPLIT' FMS AND FLT DIRECTOR IT IS DIFFICULT TO QUICKLY DETERMINE WHAT COURSE THE OTHER PLT'S FLT DIRECTOR IS FOLLOWING. EACH PLT HAS AN INDIVIDUAL FLT CTL PANEL WHERE THEY MAY CHOOSE DIFFERENT FLT DIRECTOR INPUTS. ALTHOUGH SOP IS TO HAVE BOTH FLT DIRECTORS MATCH; DURING A HIGH WORKLOAD PERIOD THIS IS NOT ALWAYS POSSIBLE. 3) AUTOPLT/FLT DIRECTOR SELECTED TO HDG NOT NAV MODE -- THE FO MAY HAVE INADVERTENTLY SELECTED HDG ON THE FCP WHILE I WAS COMPLETING THE AFTER TKOF CHKLIST AND COMMUNICATING ON THE RADIO. THIS WOULD HAVE BEEN DIFFICULT FOR ME TO SEE IMMEDIATELY SINCE MY FLT DIRECTOR WAS IN NAV MODE. WHEN WE REALIZED THAT WE HAD DEVIATED FROM COURSE THE AUTOPLT WAS IMMEDIATELY DISCONNECTED AND THE FO BEGAN PUSHING VARIOUS BUTTONS ON THE FCP IN AN EFFORT TO RESELECT THE RNAV DEP. I WAS UNABLE TO DETERMINE WHAT THE EXACT AUTOPLT/FLT DIRECTOR CONFIGN WAS ON HIS SIDE AT THE TIME OF OUR DEV. 4) FATIGUE -- BOTH THE FO AND I HAD BEEN ON MINIMUM REST THE PREVIOUS NIGHT. WE ALSO ENCOUNTERED NUMEROUS PROBS BEFORE BEGINNING OUR SEQUENCE OF TRIPS IN THE MORNING (GND TRANSPORTATION FAILED TO SHOW; 2 BROKEN GPU'S; DIFFICULTY STARTING ACFT). OUR TRIP FROM LAS WAS THE 3RD AND FINAL LEG OF THE DAY. I BELIEVE ALL THESE FACTORS MAY HAVE COMPOUNDED OUR FATIGUE AND DIMINISHED OUR CONCENTRATION AND LED TO A STATE OF COMPLACENCY LATER IN THE DAY. WE CLRLY DID NOT MONITOR THE ACFT FLT PATH AS CLOSELY AS WE SHOULD HAVE.