During a meeting over the weekend, 98 percent of the members of Broadway's musicians' union voted for a strike if they do not reach an agreement with the employers. The actors' union has also approved a strike.
None of the unions have yet declared a strike.
In the actors' dispute, which according to Hollywood Reporter mainly concerns contributions to healthcare, mediators have been called in.
The musicians have been without a collective agreement since the end of August and, like the actors, have demanded increased healthcare support, pay rises and job security.
The unions represent the majority of the actors and musicians working on Broadway, where musicals such as Wicked, Hamilton and Mamma Mia are currently being performed, and strikes from any of them could cancel several performances.