For a year and a half, middle-level officials of the Westinghouse Electric Corporation in Pittsburgh participated in a series of private and sometimes harrowing meetings with activists who had been conducting vigils against the company because of its nuclear-weapons work. But Westinghouse rebuffed the protesters' proposal that the company establish an ethical-review process on defense contracts, and the activists have continued passing out their leaflets at the company's headquarters.

MINNEAPOLIS, SEPARATED from its sister city, St. Paul, by the Mississippi River, is a green and clean community graced with lakes and parks. Many of its 365,000 people are descended from Scandinavian and German settlers. The work ethic is strong there - lots of people get to the office by 7 A.M. Honeywell, which employs 18,000 people in the area, has been a good corporate citizen for many years, supporting youth development and special-education programs and giving more than $1 million for the renovation of houses in the low-income neighborhood where its home office is located. Honeywell also produces guidance-system components for B-52 bombers and Trident and MX missiles.

When Sue Ann Martinson, a poet and Honeywell Project activist, asserts that the Government gives money to the company ''to plan for the mass murder and destruction of the world,'' the charge angers not only thousands of Minnesotans whose lives have been touched for the better by Honeywell over the years, but also many older people who still identify proudly with the World War II image of the Honeywell worker as ''the man behind the man behind the gun.''

The company had its first encounters with public protest beginning in 1969 because it was manufacturing components for cluster bombs that were killing civilians in Vietnam. The bitterness between the company and the members climaxed in 1977 with the filing of a lawsuit charging that the Federal Bureau of Investigation, working with Honeywell, had infiltrated the protest group. (Two years ago, the Federal Government and Honeywell agreed to pay $35,000 each in settlement of the suit.) After almost a decade of demonstrations, the Honeywell Project fell into quiescence. Then, in 1981, an activist of the Plowshares movement passed through the city and goaded some of the members into tak-ing the company on again because of its nuclear work.

Plowshares - whose leaders have included Daniel and Philip Berrigan - is the most audacious of the antinuclear protest groups. In more than 20 actions since 1980, Plowshares activists have invaded Government and corporate nuclear-weapons facilities and damaged nuclear missiles, submarines and airplanes with hammers; they have also poured human blood on weapons and blueprints. Some have been sentenced to as many as 18 years in prison. While their tactics have alienated elements of the broader peace movement, their influence has been critical. Says Marv Davidov, a leader of the Honeywell Project, ''They move all the rest of us.''

Spurred by the visitor from Plowshares, the Honeywell Project launched its first mass protests on the nuclear issue in 1982. Within a year, more than 1,000 people were turning out for the demonstrations. Honeywell closed its plaza to the demonstrators; they trespassed. The company took out full-page advertisements in local newspapers to present its side of the issue, arguing, for example, that ''voters, not companies, have the responsibility to determine defense decisions.''

At first, according to Anthony Bouza, the police chief, Honeywell told police, ''You're not arresting them fast enough.'' Bouza says he tried ''to strike a balance in a tortured path.'' By the end of 1986, the court system was so clogged that small groups of trespassers were being tried as ''representatives'' of larger groups.