1. A computer processor system comprising: a processor having an I-unit that fetches and decodes instructions including ESA (Enterprise System Architecture)/390 STOSM (Store Then Or System Mask) and STNSM (Store Then And System Mask) instructions and an E-unit that executes those instructions in an overlapped manner with those of the I-unit: and finish and interrupt logic that allows a ESA/390 STOSM instruction and a ESA/390 STNSM instruction to be executed normally without processor serialization or artificially extending processor execution time after execution of the ESA/390 STOSM instruction and the ESA/390 STNSM instruction and exceptionally with processor serialization after the ESA/390 STOSM instruction and the ESA/390 STNSM instruction; and a counter which is reset when executing STOSM or STNSM instructions and after being reset said counter then begins to count machine cycles, said counter being incremented on each processor clock cycle until said counter reaches a predefined value; and a mechanism which prohibits asynchronous interrupts while said counter is being incremented to count machine cycles and until said counter has reached a redefined maximum value, and wherein a program status word (PSW) ESA/390 system mask having at least 0 though 7 bits changes value by changing bits of the system mask, and wherein the processor is serialized or otherwise delayed in execution of subsequent instructions when said counter being incremented on each processor clock cycle until it reaches a predefined value is running and an I/O or external interrupt is pending regardless of the state of bits 6 or 7 in the program status word (PSW) ESA/390 system mask which are provided for use by the mechanism which prohibits asynchronous interrupts while said counter is being incremented to count machine cycles and until it has reached its predefined maximum value, and the program status word (PSW) ESA/390 system mask value changes by changing bits of the program status word ESA/390 system mask, and when STOSM or STNSM instructions are executed and changes in the values of bits 0 to 5 of the program status word (PSW) ESA/390 system mask is detected, the computer processor system immediately serializes the processor upon detected changes in the values of bits 0 to 5 of the program status word (PSW) ESA/390 system mask, and execution of the STOSM instruction causes notifies asynchronous interrupt logic of said finish and interrupt logic that a SIE (Start Interpretive Execution) Intervention Check may be required if said apparatus detects changes in bits 6 to 7 of the ESA/390 PSW or if a SIE Intervention Bypass bit in a SIE state descriptor is zero.