A circuit arrangement for bus arbitration alters the sequence in which device requests are arbitrated with respect to each other and to a previous arbitration sequence. To this end, an arbiter grants access to a first group of devices according to a predetermined sequence. The arbiter then automatically alters the sequence for a second group of devices, granting access to the bus for the second group according to the altered sequence. These features allow the order in which the arbiter sequences through the groups to be automatically varied with respect to each other, diminishing the likelihood of lockout.