A Branch in Subspace Group (BSG) instruction is executed in problem state (for example by an application program) for providing a fast instruction branch between address spaces within a restricted group of address spaces called a subspace group. The subspace group contains two types of address spaces: a base space and any number of subspaces. The subspace group is set up in a control table associated with each dispatchable unit (DU). This DU control table contains: an identifier of a base space, an identifier of an access list that contains identifiers of all subspaces in the subspace group, an indicator of whether CPU control was last given to a subspace or to the base space, and an identifier of a last entered subspace in the group. The BSG instruction has an operand defining a general register containing the target virtual address and an associated access register containing an access-list-entry token (ALET) defining the target address space. The ALET indexes to a target subspace identifier in the access list, and then the associated virtual address locates the target instruction in the identified target address space. BSG instruction execution controls restrict the BSG branching only to an instruction in the subspace group.