Does Constants use package? If not, you should be using do, not use: 

A.pm
----
# Order doesn't matter.
BEGIN { do 'Constants.pm' }
use B;

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B.pm
----
BEGIN { do 'Constants.pm' }

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use will only run the module once.

If Constants uses package, then Constants must export the constants:

A.pm
----
# Order doesn't matter.
use Constants;
use B;

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B.pm
----
use Constants;

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In reply to Re: Using constants in multiple files? by ikegami
in thread Using constants in multiple files? by Jman1

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