A typical asynchronous processing application is online inquiry on remote databases; for example, a credit rating check application. A terminal operator uses a local transaction to enter a succession of inquiries without waiting for replies. For each inquiry, the local transaction initiates a remote transaction to process the request, so that many copies of the remote transaction can be executing concurrently. The remote transactions send their replies by initiating a local transaction (possibly the same transaction) to deliver the output to the operator terminal. The replies may not arrive in the same order as the inquiries were issued; correlation between the inquiries and the replies must be made by means of fields in the user data.