The applications are from Cornelius Johannes van Wyk, serving sentences of life imprisonment on three counts of murder, and Jean Prieur du Plessis, who is serving 12 years for crimes including robbery, the theft of weapons from the SA Defence Force and illegal possession of firearms.
Van Wyk was sentenced in the Pretoria Supreme Court in September 1994 for the murders of Makoarela Dobani, Wilson Dobani and Maria Claudine Roux at Cloud's End, Louis Trichardt, in October 1991.
Du Plessis was acquitted on these counts at their trial, but both men were convicted on seven other charges arising out of their activities.
Two other members of the NSP, Johannes Jurgens Grobbelaar and Jurgen Matthews White, died after being pursued in a stolen car by the police at Noenieput, near Upington, in November 1991.
Grobbelaar's mother gave evidence at a hearing of the commission's Human Rights Violations Committee in Johannesburg in April, where she raised questions about the manner of her son's death.