FLC OF CORPORATE ACFT; C501SP HAS 2 NMACS WITHIN 30 SECONDS ON CLB OUT OF SFB ARPT. TA ISSUED BUT TFC SO CLOSE UNABLE TO AVOID WITHOUT RAPID EVASIVE ACTION.

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C501SP. ON DEP FROM SANFORD; FL; EXPERIENCED 2 NMACS WITHIN APPROX 30 SECONDS. ON IFR FLT PLAN AND WAS RELEASED BY SANFORD TWR WITH DEP INSTRUCTIONS TO CLB AND MAINTAIN 1500 FT AND TO FLY HDG 360 DEGS. UPON BEING HANDED OFF TO AND CONTACTING ORL APCH; WAS GIVEN TFC ALERT (WORDING UNCERTAIN) OF ACFT NEARBY. SAW ACFT ABOVE AND TO MY L. REDUCED PWR TO IDLE (GEAR WARNING HORN WAS BLOWING) AND WENT INTO STEEP R BANK WHILE SIMULTANEOUSLY PITCHING DOWN. RECOVERED AT APPROX 1000 FT AND BEGAN R TURN BACK TO 360 DEG HDG AND BEGAN CLBING AGAIN. WAS GIVEN ALT ASSIGNMENT OF 4000 FT AND HDG OF 040 DEGS (THESE NUMBERS FROM MEMORY AND NOT EXACT). BEGAN CLBING AGAIN AND WAS GIVEN ANOTHER TA OF ACFT AHEAD; 1 MI (MEMORY) AT 2400 FT. WAS ADVISED TO CLB RAPIDLY THROUGH THAT ALT. BEGAN TO INITIATE CLB JUST AS SECOND ACFT WAS SPOTTED. THIS ACFT FILLED WINDSHIELD. AGAIN PULLED PWR TO IDLE (GEAR WARNING HORN GOING OFF); STARTED INTO STEEP R BANK AND PITCHED DOWN. WITH APPROX 60-90 DEGS OF BANK AND PITCHING DOWN; STILL APPEARED THAT WE WOULD HIT OTHER ACFT. PUSHED HARD DOWN AND MAINTAINED DISTANCE FROM OTHER ACFT. ESTIMATE THAT WE WERE WITHIN 100 FT OF OTHER ACFT; BUT WAS HARD TO ESTIMATE BECAUSE IT HAPPENED SO RAPIDLY. ADVISED ORL APCH OF THE SECOND ACFT AND REQUESTED THAT WE BE VECTORED AROUND ANY OTHER ACFT IN THE VICINITY. IN TALKING WITH ORL APCH PERSONNEL NEXT DAY; FOUND THAT SANFORD TWR HAS NO RADAR; EVEN THOUGH IT IS A MAJOR TRAINING ARPT.