A global record (i.e. a set of local records, one for each process of
an asynchronous computation) abstracts what is usually called global s
tate, global checkpoint or global snapshot in particular problems. Con
sistent global records are important in many applications. This paper
addresses the following question: ''Given a set of local records, is i
t possible that these records belong to the same consistent global rec
ord?''. This question has been answered by Netter and Xu in the partic
ular context of message passing systems. This paper extends their resu
lt to a very general asynchronous computational model that encompasses
shared memory systems and various message passing systems (with relia
ble or unreliable and point-to-point or multicast or broadcast communi
cations).