A program authorization mechanism for authorizing access to an address space in the main memory of a computer system by a program being run under a multiple address space facility. An access-list entry is associated with each address space, each access-list entry being designated by an access-list-entry token contained in an access register. Each access-list entry includes a private indicator which indicates if the associated address space can be accessed by all programs from this access-list entry or if the associated address space can only be accessed by an authorized program. For program to be authorized, an extended authorization index in a control register must match an access-list extended authorization index in the access-list entry, or the extended authorization index value must be authorized in an authority table associated with the address space. An instruction for testing a given extended authorization index for a given access-list-entry is also disclosed.