Both Cold War era stories set in the United States in the 1950s, the films have nine nominations each and are both nominated in the best film category. (Also Read: Full List of Nominations)
They are up against financial drama The Big Short and survival tale The Revenant, which has eight nominations.
Also in the running for best film is Spotlight -- the story of the journalists who uncovered sexual abuse in the Catholic Church which led nominations of the Golden Globes along with Carol.
The awards will be announced on February 14, two weeks before the Oscars.
Irish actress Saoirse Ronan, 21, is nominated for best actress for her performance in Brooklyn, the story of an Irish immigrant to New York which has six nominations.
The other nominees for best actress are Cate Blanchett for Carol, Brie Larson for Room, Maggie Smith for The Lady in the Van and Alicia Vikander for The Danish Girl -- who is also up for best supporting actress for her role in thriller Ex Machina.
Vikander's fellow star in The Danish Girl, British actor Eddie Redmayne, who plays a transgender artist, has been nominated for best actor for the same film.
It is Eddie Redmayne's second best actor nomination in a row after winning the award last year for portraying scientist Stephen Hawking in The Theory of Everything.
Eddie Redmayne will be up against Leonardo DiCaprio for The Revenant, Michael Fassbender for Steve Jobs, Matt Damon for The Martian and Trumbo star Bryan Cranston -- known for his leading role in television hit Breaking Bad.
In the best director category, Steven Spielberg is up against Mexico's Alejandro Gonzalez Inarritu, Britain's Ridley Scott, and US directors Adam McKay and Todd Haynes.
The main nominations:
The Big Short
Bridge of Spies
Outstanding British film
The Danish Girl
Adam McKay for The Big Short
Steven Spielberg for Bridge of Spies
Todd Haynes for Carol
Ridley Scott for The Martian
Alejandro Gonzalez Inarritu for The Revenant
Bryan Cranston for Trumbo
Matt Damon for The Martian
Leonardo DiCaprio for The Revenant
Michael Fassbender for Steve Jobs
Eddie Redmaybe for The Danish Girl
Cate Blanchett for Carol
Brie Larson for Room
Saoirse Ronan for Brooklyn
Maggie Smith for The Lady in the Van
Alicia Vikander for The Danish Girl
Christian Bale for The Big Short
Benicio del Toro for Sicario
Idris Elba for Beasts of No Nation
Mark Ruffalo for Spotlight
Mark Rylance for Bridge of Spies
Jennifer Jason Leigh for The Hateful Eight
Rooney Mara for Carol
Alicia Vikander for Ex Machina
Julie Walters for Brooklyn
Kate Winslet for Steve Jobs