In one embodiment, a data processing system (10) has a processor (14) coupled to a bus, where the data processing system (10) includes access error detection circuitry (26) and access error response circuitry (12), each coupled to the bus (58, 60). The access error detection circuitry detects an access error in the data processing system. The access error response circuitry initiates replacement of an existing value on the bus with a predetermined value when the access error has been detected, and continues to replace the existing value on the bus with the predetermined value when the access error has been detected and a persistent mode indicator has been asserted. The predetermined value may correspond to a predetermined instruction value (74) or a predetermined data value (76). In one embodiment, different values for the predetermined value may be used depending on the current operating mode of the data processing system.