The Civil Aeronautics Board yesterday tentatively awarded Evergreen International Airlines new nonstop authority to fly from the Washington area to the Yucatan Peninsula in Mexico.

Earl Tawney, Evergreen's vice president for scheduled services, said yesterday the airline has plans to begin nonstop service to the Yucatan from Baltimore/Washinton Internatinal Airport the first week in November at fares about 20 percent below those of its competitors. Evergreen will be the only airline allowed to fly nonstop to the Yucatan from here, under terms of the U.S. -- Mexico air services bilateral agreement which limits major routes to a single U.S. airline.

Until airline deregulation presented it with new opportunities to apply for new routes as a scheduled airline, Evergreen carried cargo and passengers only on charters. In February it began scheduled airline service from Philadelphia to Freeport in the Bahamas, and last month it began once-a-week service to Freeport from BWI. The BWI-Freeport service is doing very well, Tawney said.

The Washington-Yucatan route award to Evergreen was one of eight Yucatan awards the board tentatively made yesterday. All must go to the president for his approval because they involve foreign routes.

Evergreen also won the CAB's endorsement for new nonstop authority from New York and Cleveland; United Airlines will get a new route from Chicago; Braniff International gets the route from Dallas/Fort Worth; Republic Airlines gets Detroit authority; and Eastern Airlines got authority to fly from Atlanta and Miami.