The top two executives of the New York State Thruway Authority abruptly quit this week, the latest sign of turmoil at the agency as it faces a deep budget shortfall and difficulty financing the construction of a new Tappan Zee Bridge.

The authority’s executive director, Thomas J. Madison, and its chief operating and financial officer, John M. Bryan, resigned without warning on Wednesday and surprised the authority’s board of directors, said Donna J. Luh, the acting chairwoman.

“We were caught off guard like everyone else was,” Ms. Luh said during a telephone interview on Thursday. “Both have done a very good job.”

Their departures followed the resignation in early December of Howard P. Milstein as chairman of the authority’s board and the announcement two weeks ago that the authority faced a deficit of $36 million for 2015.