A method performed within a multi-processing, multi-programming computer environment for reducing conflict among tasks concurrently accessing COMMON BLOCKs in code sequences compiled within said environment from a FORTRAN like language system, and for reducing the memory used in the storing of private copies of said COMMON BLOCKs. The method involves inserting constructs at compile time into the compiled code which enable the COMMON BLOCKs to be dynamically bound at runtime to two or more referencing tasks. Then, at execution time responsive to the constructs, the blocks are bound to the tasks dynamically and scoped so that they lie within the dynamic nesting of the tasks.