Additional information to the 2 before:
In ASME IIA, you can find a chapter "Acceptable ASTM editions" (page xlvii), giving details about the allowed ASTM grades in function of the design code and the acceptable editions. Not all editions are acceptable. E.g. up to Addenda 06, ASTM A516 edition 90 was acceptable and not the more recent editions 03, 05, 06. At my experience, this assures that the used ASTM edition is 100% identical to the current ASME edition. In the ASME material standard, you always find the indication, to which edition of ASTM it is identical. But the easiest way is, as said by JStephen, to stay with ASME grades when material is used for ASME applications.