CAPT OF A CESSNA CITATION V C560 ALLOWED THE ACFT TO DSND BELOW ASSIGNED ALT DURING DEP CAUSING A LOW ALT ALERT BY ATC. AFTER CAPT REALIZED HIS ERROR AND RETURNED TO ASSIGNED ALT; ATC QUESTIONED HIS ALT.

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ON DEP FROM TEB; UPON LEVELING OUT AT 1500 FT AGL AND BEING REQUESTED TO TURN L APPROX 180 DEGS IN LIGHT TO MODERATE RAIN SHOWERS; WITH LIGHT TO MODERATE TURB; WHILE BEING DISTR BY THE FO'S INABILITY TO HANDLE ATC COM AND NAV; WE ENCOUNTERED AN ALTDEV. BECAUSE OF MY DISTR IT WAS NOT DETECTED IMMEDIATELY BUT WAS DETECTED QUICKLY AND AFTER LOSING 300-400 FT I RE-ESTABLISHED A POSITIVE CLB RATE AND CONTINUED THE FLT UNEVENTFULLY. PAX AND FO WERE UNAWARE OF THE DEV. UPON REACHING 1500 FT OR SO; AGAIN ATC ASKED OUR ALT; SO WE MAY HAVE CAUSED SOME LOW RETURN; BUT BY THEN PROB CORRECTED. HOWEVER; BECAUSE I DIDN'T SEE THE START OF THE DSCNT; I'M NOT SURE IF I HAD WINDSHEAR OR A DOWNDRAFT OR NOT. FORTUNATELY; MY SCAN WAS FAST ENOUGH. HOWEVER; IF MY ATTN HAD NOT BEEN DIVIDED; I MIGHT HAVE DETECTED THE PROB EVEN SOONER AND POSSIBLY AVOIDED IT ALTOGETHER. FURTHER; IF MY FO HAD BEEN PULLING HIS SHARE OF THE WORKLOAD; OR IF I HAD PUT THE AUTOPLT ON; I WOULD HAVE MAYBE DETECTED THE ALT LOSS SOONER. THE ODD THING IS THERE WAS NO NEGATIVE PITCH CHANGE AND NO SUDDEN OR RATHER ABRUPT PERCEPTIBLE DOWNWARD PUSH AND NO EXCESSIVE BANK ANGLE -- JUST A DEFINITE DOWN TREND ON THE VSI'S AND ALTIMETER.