"Tomorrow Never Comes" was recorded in 1944 by Ernest Tubb and released as single on Decca 6106 the following year.

As we can see on the label, Ernest Tubb composed the song and Johnny Bond wrote the lyrics. It reached #3 in 1945.
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Johnny Bond - the writer of the lyrics - recorded the song himself as well, though some 25 years later. It was released in January 1970.
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It's possible that the lyrics inspired Hank Williams in 1946 to write I Don't Care (If Tomorrow Never Comes). Singer Molly O'Day recorded it first. The song, a lament about a lost love, was recorded at Williams' second and final Sterling recording session on February 13, 1947 with Tommy Jackson (fiddle), Dale "Smokey" Lohman (steel guitar), Zeke Turner (electric guitar), and Louis Innis (bass)
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Other versions of Tomorrow Never Comes:
Recorded on March 19, 1958 by Skeets Mc Donald:
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In the arrangement which inspired Elvis, with Roy Orbison's "Running Scared" beginning. Glenn Campbell as released in March 1963:
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B.J. Thomas recorded it in 1965, with a beginning which reminds me of Elvis' version of You've Lost That Lovin' Feelin'. Another inspiration for Elvis?
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A woman's take on the song. Dottie West in 1970:
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Elvis recorded his version during the Marathon sessions on June 7, 1970. Elvis on top of his game. Here's the undubbed take 2 of the song:
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The undubbed Master (take 13):
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And the Master as how it finally was released on Elvis Country, sanse the I'm 10,000 Years Old overdub.
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A That's The Way It Is rehearsal of the song:
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Sources
http://davidneale.eu/elvis/originals/list9.html#S1517
https://en.wikipedia.org/wiki/Tomorrow_Never_Comes_(Ernest_Tubb_song)
https://secondhandsongs.com/work/40237/all
https://en.wikipedia.org/wiki/I_Don%27t_Care_(If_Tomorrow_Never_Comes)