If the poster is going to be "matted & framed", I'd use "acid-free" papers (this is also known as "Archival"). The process used to manufacture said papers minimizes the chemicals associated with "yellowing" of photos/posters etc.
...c'mon, I'm not a scientist; this is just something I learned working at an art-supply store a while back.
Foxing is your biggest problem, like in the Velo Sport poster above. Mostly because it can really work fast. The above information is all pretty good, but if you poster was printed on non-acid-free paper you'll always have a potential problem.
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