just occurred to me, but i am not sure if this is exactly what is meant
Of course one of the most famous art museums in the world is "The Museum of Modern Art"

I would say

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Note added at 6 hrs (2006-02-15 14:26:30 GMT)
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What makes Art Contemporary?
Craig Judd, 2000
For artists the word 'contemporary' refers to objects made today or within the last few months to a year. For curators or critics, contemporary refers to a looser chronology stretching over a couple of years. For art historians and other cultural commentators, contemporary art begins in 1945, post–WWII, with the rise of Abstract Expressionism, or with the shock of Pop art in the early 1960s. However, there is now a general consensus that contemporary art refers to art made after 1970.

Penny McKeon, 2000
The contemporary is a moveable artworld category. All art was contemporary at some point; over time it enters the domain of the historical past. 'Contemporary' has been defined in various ways. The Museum of Modern Art in New York initially regarded contemporary as referring to works produced in the past 50 years. Some writers define contemporary art as the art of our lifetime; for students this would mean the art of the past 10-15 years. Artworld literature also uses various boundaries, for example, the art produced post-1945, after WW11. More recent surveys consider art created since 1960 or 1980 to constitute the contemporary.

Isobel Crombie, 1996
[Contemporary art] is the art of now; it is the art that surrounds us; it is often a true expression of contemporary sentiments.
http://www.vceart.com/explore/ideas/page.4.html