EMP145 PLT RPTS ATL TOWER ISSUED LOW ALTITUDE ALERTS WHEN ACFT WAS ON A VISUAL APCH BUT AT OR ABOVE PUBLISHED INSTRUMENT ALTITUDES FOR THE RWYS IS USE.

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ON APR/SAT/07 AT APPROX XA25 DURING OUR ARR INTO ATL; WE WERE GIVEN VECTORS AND AN ALT OF 3500 FT TO INTERCEPT THE LOC FOR RWY 26R. THE WX WAS VFR (CLR BELOW 12000 FT; VISIBILITY +10 SM). WE CALLED ARPT IN SIGHT AND WERE CLRED FOR THE VISUAL RWY 26R. AT THE SAME TIME THE AUTOPLT CAPTURED THE LOC; BECAUSE WE WERE ABOVE THE GS WHEN CLRED FOR THE VISUAL. WE DIALED AN ALT OF 2700 FT (INTERCEPT ALT AT THE OM -- AJAAY) AND WENT VERT SPD DOWN TO CAPTURE THE GS. ATL TWR THEN GAVE US AN ALT ALERT. AGAIN ON APR/SAT/07 AT APPROX XF55 ON THE SAME ARR FROM THE SAME DIRECTION WE WERE GIVEN VECTORS TO THE VISUAL RWY 26R. WE WERE CLRED DOWN TO 2700 FT AT 9 DME (2.3 DME OUTSIDE OF AJAAY) WE INTERCEPTED THE LOC AND RECEIVED AN ALT ALERT FROM ATL TWR. WE VERIFIED 2700 FT WITH TWR; THEY CONFIRMED AND THOUGHT THE ALERT MIGHT HAVE BEEN CAUSED BECAUSE WE WERE IN A TURN. I AM NOT EXACTLY SURE WHY WE RECEIVED AN ALT ALERT. AFTER RECEIVING THE FIRST ONE; WHICH CAUGHT US OFF GUARD; WE PAID SPECIAL ATTN TO OUR EXACT DME AND ALT DURING OUR SECOND VISUAL TO RWY 26R. IN BOTH CASES SAFETY WAS NEVER COMPROMISED. BOTH ALERTS WERE ISSUED AT 2700 FT AROUND 2 DME OUTSIDE THE OM IN A TURN. 2700 FT IS THE GS INTERCEPT ALT. BOTH VISUALS WERE ALSO SHORT APCHS.