|- ! | William T. Cahill | | Republican | 1958 | Incumbent re-elected. | nowrap | |- ! | Milton W. Glenn | | Republican | 1957 | Incumbent re-elected. | nowrap | |- ! | James C. Auchincloss | | Republican | 1942 | Incumbent re-elected. | nowrap | |- ! | Frank Thompson | | Democratic | 1954 | Incumbent re-elected. | nowrap | |- ! | Peter Frelinghuysen Jr. | | Republican | 1952 | Incumbent re-elected. | nowrap | |- ! | Florence P. Dwyer | | Republican | 1956 | Incumbent re-elected. | nowrap | |- ! | William B. Widnall | | Republican | 1950 | Incumbent re-elected. | nowrap | |- ! | Gordon Canfield | | Republican | 1940 | | Incumbent retired.New member elected.Democratic gain. | nowrap | |- ! | Frank C. Osmers Jr. | | Republican | 1951 | Incumbent re-elected. | nowrap | |- ! | Peter W. Rodino | | Democratic | 1948 | Incumbent re-elected. | nowrap | |- ! | Hugh Joseph Addonizio | | Democratic | 1948 | Incumbent re-elected. | nowrap | |- ! | George M. Wallhauser | | Republican | 1958 | Incumbent re-elected. | nowrap | |- ! | Cornelius Gallagher | | Democratic | 1958 | Incumbent re-elected. | nowrap | |- ! | Dominick V. Daniels | | Democratic | 1958 | Incumbent re-elected. | nowrap | |} New Mexico |- ! | Joseph Montoya | | Democratic | 1957 | Incumbent re-elected. | rowspan=2 nowrap | |- ! | Thomas G. Morris | | Democratic | 1958 | Incumbent re-elected. |} New York |- ! | Stuyvesant Wainwright | | Republican | 1952 | | Incumbent lost re-election.New member elected.Democratic gain. | nowrap | |- ! | Steven Derounian | | Republican | 1952 | Incumbent re-elected. | nowrap | |- ! | Frank J. Becker | | Republican | 1952 | Incumbent re-elected. | nowrap | |- ! | Seymour Halpern | | Republican | 1958 | Incumbent re-elected. | nowrap | |- ! | Albert H. Bosch | | Republican | 1952 | | Retired to run for judge of Queens County court.New member elected.Democratic gain. | nowrap | |- ! | Lester Holtzman | | Democratic | 1952 | Incumbent re-elected. | nowrap | |- ! | James J. Delaney | | Democratic