They joined Lanny Wadkins, the Ryder Cup captain, the former US Open champions Hale Irwin and Ray Floyd, and Rocco Mediate on the list of Americans exempt from qualifying to pull out of the event. Several more have withdrawn from final qualifying.
Couples, the 1992 Masters champion, told organisers he had been advised that the back injury which kept him out of action for several months this year had not healed sufficiently for him to make the trip.
Couples, ranked fifth in the world, played in some recent US Tour events even though he was not fully fit. Strange, the 1988 and 1989 US Open champion, said only that he had decided not to play.
Another top American, world No 10 Paul Azinger, did not enter because he is recovering from cancer. He is expected to rejoin the US Tour later this year.
Michael Bonallack, the secretary of the Royal and Ancient Club who stage the Open, expressed regret at the withdrawals but he was upbeat about the field.
'Clearly we are disappointed that Fred and Curtis are unable to be with us at Turnberry,' Bonallack said.
'However, we do sympathize greatly with the back problems Fred has faced this season, and it is still very encouraging that 45 of the world's top 50 will still contest the championship.'
The withdrawal of Couples and Strange means that there are now no Americans in the nine favourites for the Open, according to the bookmakers William Hill.
They have Greg Norman, the defending champion, out in front at 10-1, with Nick Faldo 12-1 and Jose-Maria Olazabal and Ernie Els, winner of the US Masters and US Open this season, 14-1 along with Bernhard Langer and Nick Price.
Scotland's Colin Montgomerie is next after that and the first US players to appear in the betting are Corey Pavin, Phil Mickelson, Tom Kite and Tom Lehman at 33-1.
Turnberry is best remembered for the Tom Watson-Jack Nicklaus birdie shoot-out in 1977 - both will be present again this week - but in 1986 many players left unhappy with narrow fairways and fierce rough.
The victory by the South African Ernie Els in the US Open has won him the Johnnie Walker Golfer of the Month award for June. The 24-year-old made history by becoming the first member of the European Tour to capture the title. Tony Jacklin's 1970 win came five years before the tour was formed.Reuse content