Things that are obsolete are out of date or no longer in general use. Things that are obsolescent are fading from general use and soon to become obsolete. For example, the Windows XP operating system (released in 2001) is not obsolete because some people still use it, but it is obsolescent because it will presumably be falling out of use in the coming years.
Things that are obsolete are usually not so out of date that they’ve been forgotten, however. When obsolete things are forgotten, they become archaic.
Because things that are obsolescent are becoming obsolete, phrases such as becoming obsolescent are redundant.
In 1998, an estimated 20 million computers became obsolete every year. [Forbes]
Some proponents have said laws and state agencies that protect workers render unions obsolete. [letter to Indianapolis Star]
In five years, Facebook will be obsolete; and in 10 years, we will harvest electricity from the oceans with underwater kites. [WZZM]
The NHS is a rambling nationalised industry in which much is spent on obsolescent services and the scarce time of experienced professionals is used poorly. [Telegraph]
The idea that war is obsolescent may seem preposterously utopian. [New York Times]
The U.S. Coast Guard will risk a drop in readiness to fulfill its top priority — replacing obsolescent ships and planes — within its slimmed-down 2011 budget … [Washington Post]