Both productions have 11 nominations.
The smash-hit Paddington the Musical, written by Tom Fletcher from British band McFly recently dominated at the WhatsOnStage awards and has received rave reviews since opening at the Savoy Theatre in London in December.
It is adapted from the books by Michael Bond and later hit films and follows the adventures of the marmalade-loving bear from Peru, starring a life-like puppet of Paddington.
Paddington's nominations include best new musical, best actor in a musical for both James Hameed and Arti Shah – who jointly perform the role of the bear – two nominations for best actress in a supporting role in a musical (Amy Booth-Steel and Victoria Hamilton-Barritt), the Sir Peter Hall award for best director (Luke Sheppard), and best set design.
It is up against The Woods in many categories, including best actor in a musical (Jamie Parker), two nominations for best actor in a supporting role in a musical (Jo Foster and Oliver Savile), and the Sir Peter Hall Award for best director (Jordan Fein).
Meanwhile, Australian Cate Blanchett will battle it out for best actress against Rosamund Pike, Marianne Jean-Baptiste, Julia McDermott and Rosie Sheehy.
Blanchett has received a nod for her role in The Seagull at the Barbican Theatre, while Pike's is for Inter Alia at the National Theatre, and Sheehy is nominated for Guess How Much I Love You, her second in a row following her nomination for last year's Machinal.
American film star Rachel Zegler has been nominated for best actress in a musical for her West End debut in the lead role in Evita at the London Palladium.
The critically acclaimed performance drew large outdoor crowds while she sang Don't Cry For Me Argentina from an outside balcony.
The most nominated plays are All My Sons, Kenrex and Stereophonic, with six each, while the nominees for best actor include Bryan Cranston, Sean Hayes, Tom Hiddleston, Jack Holden and David Shields.
Hiddleston is up for best actor for Much Ado About Nothing at Theatre Royal Drury Lane, while Cranston receives a nod for All My Sons, which is playing at Wyndham's Theatre.
All My Sons has also received nods for best revival, best actress for Jean-Baptiste, best actress in a supporting role (Hayley Squires), and the Sir Peter Hall Award for best director (Ivo van Hove).
Among its six nominations, Kenrex is up for best new play, best actor (Jack Holden), the Sir Peter Hall Award for best director (Ed Stambollouian), and outstanding musical contribution (John Patrick Elliott for composition).
This year's Olivier Awards will mark the 50th anniversary of the ceremony, and will be hosted by comedian Nick Mohammed at the Royal Albert Hall.
