For thousands of Washington area government workers, a day at the office can mean headaches, sore throats, watering eyes and dizzy spells.

Some employes believe their health is being endangered by auto exhaust fumes that seep up stairwells and elevator and ventilating shafts that connect with garages in their buildings.

Two agencies here - Agriculture and the Equal Employment Opportunity Commission - have moved or plan to shift employes from offices where complaints of bad air have caused work problems.

Twice this year, the EEOC has sent workers home early on paid leave because of fumes believed to be coming from a first-floor parking area at their Columbia Plaza office building in the city.

In Arlington, officials of the international development staff of the Agriculture Department have recommended that employes be moved from a second-floor office in the Pomponio building until the problem can be cleared up.

Some EEOC workers today are planning a lunch-time informational picket line to protest "inadequate action" to correct problems that they say have resulted in employes' regularly getting sick at the office. The American Federation of Government Employes local at EEOC is planning the demonstration.

Spokeswoman Shari Danch, who is an EEOC worker, says employes may sue both their agency and the General Services Administration for failure to correct what they view as a health problem.

GSA, the government's landlord agency, rents the Columbia Plaza building from Shannon and Luchs for work space for EEOC and Treasury, State and Interior department employes.

GSA officials say they have been monitoring the problem, and have not detected "dangerous" levels of carbon monoixde. They plan to call in a private firm, Enviro Control Inc. of Rockville, to survey the air quality in the building next week.

During March 28-29, Enviro conducted a survey of the Pomponia Plaza building for the Agriculture Department. The 12-story structure also houses units of the Navy, Defense Intelligence Agency and State Department.

GSA and managers of the building - ALGIN Management Co. - say nobody at Agriculture has complained about exhaust fumes since early in March when a walk-through inspection was made. At that time an employe complained, they say, and the problem was traced to an open door leading to the basement parking garage. Since then, both GSA and the landlord say they have had no complaints from any of the tenants.

The Enviro report of the Agriculture offices said that air samples taken there found concentrations of carbon monoxide that were "significantly below" allowable levels. That is, the air was found to be relatively safe.

But it did say that the levels of "carbon monoxide contamination" found in some Agriculture offices "are great enough to be causing the symptoms expressed by office employes." Those symptoms include headaches and eye and upper respiratory irritation.

On April 10, William S. Hoofnagle, deputy director of the Agriculture unit, wrote superiors asking that "action be taken to relocate us in other quarters free from fumes and ones more conducive to the work" of the agency. Agriculture officials say they are now looking for space to put the employes.

The Columbia Plaza building is leased to the government for 20 years at an annual rental of $2.3 million. It has inside parking spaces for 346 cars, and officials say that improved ventilation and a rescheduling of garbage pickups to the early morning should clear up any problem. Meantime, the EEOC has moved some employes to higher floors.

Rent for the Pomponio Plaza building has just been renegotiated at $1.5 million a year, GSA officials said, on a three-year lease. Parking there is for 205 cars.

GSA officials say that employes often complain about air pollution problems, but don't bring it to the attention of GSA or the building manager. An official said that similar problems were corrected at the new Labor Department building that straddles the I-95 freeway. It got heavy doses of auto exhaust fumes before a "positive pressure" system was installed to blow away bad air.

A federal health official said that spot monitoring through "industrial hygiene surveys" doesn't always pick up carbon monoxide problems. He said the gas is odorless, tasteless and invisible. Agencies need to monitor conditions during morning and evening rush hour buildups, he believes, when car motors are running and traffic is stalled, and also when meteorological inversions trap air and can cause stagnation.

"It may take a nasty lawsuit," a union official said, "to persuade the bosses - who are usually on upper level floors or never at the office - that we don't want to be gradually gassed by 'tolerable' levels of carbon monoxide.'