New York and Massachusetts are following the federal health exchange’s lead and extending their sign-up deadlines for coverage starting Jan. 1, those programs’ directors announced Monday afternoon.

Other state exchanges, including the ones in California, Washington state and the District of Columbia, are offering general flexibility for individuals who started but couldn’t complete their applications by the 11:59 p.m. Monday deadline. Residents there will still be guaranteed coverage starting Jan. 1.

By contrast, Connecticut and Colorado announced Monday that their exchanges were holding to Dec. 23 as the enrollment cut-off.

New Yorkers now will have until 11:55 p.m. Christmas Eve to choose a plan, said officials, who described “very high enrollment activity” Monday.