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| Date | Title | Country | Details |
|---|---|---|---|
| 1/4 | There! I've Said It AgainDetailsArtist: Bobby Vinton · Weeks at No. 1 that month: 4 | United States | Artist: Bobby Vinton · Weeks at No. 1 that month: 4 |
| 2/1 | I Want to Hold Your HandDetailsArtist: The Beatles · Weeks at No. 1 that month: 5 | United States | Artist: The Beatles · Weeks at No. 1 that month: 5 |
| 3/7 | I Want to Hold Your HandDetailsArtist: The Beatles · Weeks at No. 1 that month: 2 | United States | Artist: The Beatles · Weeks at No. 1 that month: 2 |
| 3/21 | She Loves YouDetailsArtist: The Beatles · Weeks at No. 1 that month: 2 | United States | Artist: The Beatles · Weeks at No. 1 that month: 2 |
| 4/4 | Can't Buy Me LoveDetailsArtist: The Beatles · Weeks at No. 1 that month: 4 | United States | Artist: The Beatles · Weeks at No. 1 that month: 4 |
| 5/2 | Can't Buy Me LoveDetailsArtist: The Beatles · Weeks at No. 1 that month: 1 | United States | Artist: The Beatles · Weeks at No. 1 that month: 1 |
| 5/9 | Hello, Dolly!DetailsArtist: Louis Armstrong · Weeks at No. 1 that month: 1 | United States | Artist: Louis Armstrong · Weeks at No. 1 that month: 1 |
| 5/16 | My GuyDetailsArtist: Mary Wells · Weeks at No. 1 that month: 2 | United States | Artist: Mary Wells · Weeks at No. 1 that month: 2 |
| 5/30 | Love Me DoDetailsArtist: The Beatles · Weeks at No. 1 that month: 1 | United States | Artist: The Beatles · Weeks at No. 1 that month: 1 |
| 6/6 | Chapel of LoveDetailsArtist: The Dixie Cups · Weeks at No. 1 that month: 3 | United States | Artist: The Dixie Cups · Weeks at No. 1 that month: 3 |
| 6/27 | A World Without LoveDetailsArtist: Peter and Gordon · Weeks at No. 1 that month: 1 | United States | Artist: Peter and Gordon · Weeks at No. 1 that month: 1 |
| 7/4 | I Get AroundDetailsArtist: The Beach Boys · Weeks at No. 1 that month: 2 | United States | Artist: The Beach Boys · Weeks at No. 1 that month: 2 |
| 7/18 | Rag DollDetailsArtist: The Four Seasons · Weeks at No. 1 that month: 2 | United States | Artist: The Four Seasons · Weeks at No. 1 that month: 2 |
| 8/1 | A Hard Day's NightDetailsArtist: The Beatles · Weeks at No. 1 that month: 2 | United States | Artist: The Beatles · Weeks at No. 1 that month: 2 |
| 8/15 | Everybody Loves SomebodyDetailsArtist: Dean Martin · Weeks at No. 1 that month: 1 | United States | Artist: Dean Martin · Weeks at No. 1 that month: 1 |
| 8/22 | Where Did Our Love GoDetailsArtist: The Supremes · Weeks at No. 1 that month: 2 | United States | Artist: The Supremes · Weeks at No. 1 that month: 2 |
| 9/5 | The House of the Rising SunDetailsArtist: The Animals · Weeks at No. 1 that month: 3 | United States | Artist: The Animals · Weeks at No. 1 that month: 3 |
| 9/26 | Oh, Pretty WomanDetailsArtist: Roy Orbison · Weeks at No. 1 that month: 1 | United States | Artist: Roy Orbison · Weeks at No. 1 that month: 1 |
| 10/3 | Oh, Pretty WomanDetailsArtist: Roy Orbison · Weeks at No. 1 that month: 2 | United States | Artist: Roy Orbison · Weeks at No. 1 that month: 2 |
| 10/17 | Do Wah Diddy DiddyDetailsArtist: Manfred Mann · Weeks at No. 1 that month: 2 | United States | Artist: Manfred Mann · Weeks at No. 1 that month: 2 |
| 10/31 | Baby LoveDetailsArtist: The Supremes · Weeks at No. 1 that month: 1 | United States | Artist: The Supremes · Weeks at No. 1 that month: 1 |
| 11/7 | Baby LoveDetailsArtist: The Supremes · Weeks at No. 1 that month: 3 | United States | Artist: The Supremes · Weeks at No. 1 that month: 3 |
| 11/28 | Leader of the PackDetailsArtist: The Shangri-Las · Weeks at No. 1 that month: 1 | United States | Artist: The Shangri-Las · Weeks at No. 1 that month: 1 |
| 12/5 | RingoDetailsArtist: Lorne Greene · Weeks at No. 1 that month: 1 | United States | Artist: Lorne Greene · Weeks at No. 1 that month: 1 |
| 12/12 | Mr. LonelyDetailsArtist: Bobby Vinton · Weeks at No. 1 that month: 1 | United States | Artist: Bobby Vinton · Weeks at No. 1 that month: 1 |
| 12/19 | Come See About MeDetailsArtist: The Supremes · Weeks at No. 1 that month: 1 | United States | Artist: The Supremes · Weeks at No. 1 that month: 1 |
| 12/26 | I Feel FineDetailsArtist: The Beatles · Weeks at No. 1 that month: 1 | United States | Artist: The Beatles · Weeks at No. 1 that month: 1 |