Paul Everette Woodward is to be executed Wednesday at the State Penitentiary at Parchman. Gerald James Holland is to be put to death Thursday.
Defense attorneys for both inmates had filed papers with the court seeking to halt the execution. Justices issued orders Monday either denying or dismissing the motions.
Woodward, who's now 62, was sentenced to death for the 1986 rape and shooting death of 24-year-old Rhonda Crane of Escatawpa.
Holland, of Adams County, was sentenced to death for raping and killing 15-year-old Krystal King in 1987. Now 72, Holland is the oldest death-row inmate in Mississippi.