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| Date | Title | Country | Details |
|---|---|---|---|
| 1/2 | Are You Lonesome Tonight?DetailsArtist: Elvis Presley · Weeks at No. 1 that month: 1 | United States | Artist: Elvis Presley · Weeks at No. 1 that month: 1 |
| 1/9 | Wonderland by NightDetailsArtist: Bert Kaempfert · Weeks at No. 1 that month: 3 | United States | Artist: Bert Kaempfert · Weeks at No. 1 that month: 3 |
| 1/30 | Will You Love Me TomorrowDetailsArtist: The Shirelles · Weeks at No. 1 that month: 1 | United States | Artist: The Shirelles · Weeks at No. 1 that month: 1 |
| 2/6 | Will You Love Me TomorrowDetailsArtist: The Shirelles · Weeks at No. 1 that month: 1 | United States | Artist: The Shirelles · Weeks at No. 1 that month: 1 |
| 2/13 | CalcuttaDetailsArtist: Lawrence Welk · Weeks at No. 1 that month: 2 | United States | Artist: Lawrence Welk · Weeks at No. 1 that month: 2 |
| 2/27 | Pony TimeDetailsArtist: Chubby Checker · Weeks at No. 1 that month: 1 | United States | Artist: Chubby Checker · Weeks at No. 1 that month: 1 |
| 3/6 | Pony TimeDetailsArtist: Chubby Checker · Weeks at No. 1 that month: 2 | United States | Artist: Chubby Checker · Weeks at No. 1 that month: 2 |
| 3/20 | SurrenderDetailsArtist: Elvis Presley · Weeks at No. 1 that month: 2 | United States | Artist: Elvis Presley · Weeks at No. 1 that month: 2 |
| 4/3 | Blue MoonDetailsArtist: The Marcels · Weeks at No. 1 that month: 3 | United States | Artist: The Marcels · Weeks at No. 1 that month: 3 |
| 4/24 | RunawayDetailsArtist: Del Shannon · Weeks at No. 1 that month: 1 | United States | Artist: Del Shannon · Weeks at No. 1 that month: 1 |
| 5/1 | RunawayDetailsArtist: Del Shannon · Weeks at No. 1 that month: 3 | United States | Artist: Del Shannon · Weeks at No. 1 that month: 3 |
| 5/22 | Mother-in-LawDetailsArtist: Ernie K-Doe · Weeks at No. 1 that month: 1 | United States | Artist: Ernie K-Doe · Weeks at No. 1 that month: 1 |
| 5/29 | Travelin' ManDetailsArtist: Ricky Nelson · Weeks at No. 1 that month: 1 | United States | Artist: Ricky Nelson · Weeks at No. 1 that month: 1 |
| 6/5 | Running ScaredDetailsArtist: Roy Orbison · Weeks at No. 1 that month: 1 | United States | Artist: Roy Orbison · Weeks at No. 1 that month: 1 |
| 6/12 | Travelin' ManDetailsArtist: Ricky Nelson · Weeks at No. 1 that month: 1 | United States | Artist: Ricky Nelson · Weeks at No. 1 that month: 1 |
| 6/19 | Moody RiverDetailsArtist: Pat Boone · Weeks at No. 1 that month: 1 | United States | Artist: Pat Boone · Weeks at No. 1 that month: 1 |
| 6/26 | Quarter to ThreeDetailsArtist: U.S. Bonds · Weeks at No. 1 that month: 1 | United States | Artist: U.S. Bonds · Weeks at No. 1 that month: 1 |
| 7/3 | Quarter to ThreeDetailsArtist: U.S. Bonds · Weeks at No. 1 that month: 1 | United States | Artist: U.S. Bonds · Weeks at No. 1 that month: 1 |
| 7/10 | Tossin' and Turnin'DetailsArtist: Bobby Lewis · Weeks at No. 1 that month: 4 | United States | Artist: Bobby Lewis · Weeks at No. 1 that month: 4 |
| 8/7 | Tossin' and Turnin'DetailsArtist: Bobby Lewis · Weeks at No. 1 that month: 3 | United States | Artist: Bobby Lewis · Weeks at No. 1 that month: 3 |
| 8/28 | Wooden HeartDetailsArtist: Joe Dowell · Weeks at No. 1 that month: 1 | United States | Artist: Joe Dowell · Weeks at No. 1 that month: 1 |
| 9/4 | MichaelDetailsArtist: The Highwaymen · Weeks at No. 1 that month: 2 | United States | Artist: The Highwaymen · Weeks at No. 1 that month: 2 |
| 9/18 | Take Good Care of My BabyDetailsArtist: Bobby Vee · Weeks at No. 1 that month: 2 | United States | Artist: Bobby Vee · Weeks at No. 1 that month: 2 |
| 10/2 | Take Good Care of My BabyDetailsArtist: Bobby Vee · Weeks at No. 1 that month: 1 | United States | Artist: Bobby Vee · Weeks at No. 1 that month: 1 |
| 10/9 | Hit the Road JackDetailsArtist: Ray Charles · Weeks at No. 1 that month: 2 | United States | Artist: Ray Charles · Weeks at No. 1 that month: 2 |
| 10/23 | Runaround SueDetailsArtist: Dion · Weeks at No. 1 that month: 2 | United States | Artist: Dion · Weeks at No. 1 that month: 2 |
| 11/6 | Big Bad JohnDetailsArtist: Jimmy Dean · Weeks at No. 1 that month: 4 | United States | Artist: Jimmy Dean · Weeks at No. 1 that month: 4 |
| 12/4 | Big Bad JohnDetailsArtist: Jimmy Dean · Weeks at No. 1 that month: 1 | United States | Artist: Jimmy Dean · Weeks at No. 1 that month: 1 |
| 12/11 | Please Mr. PostmanDetailsArtist: The Marvelettes · Weeks at No. 1 that month: 1 | United States | Artist: The Marvelettes · Weeks at No. 1 that month: 1 |
| 12/18 | The Lion Sleeps TonightDetailsArtist: The Tokens · Weeks at No. 1 that month: 2 | United States | Artist: The Tokens · Weeks at No. 1 that month: 2 |