A white farm couple and their two grandchildren were killed by dissidents, the government announced today, in a move that shows that massive Army sweeps in southwestern Zimbabwe have not eliminated armed resistance to the government.

The killings last night 13 miles north of Bulawayo were the worst single dissident incident since troops launched a major offensive in Matabeleland in late January against the armed men, mainly Army deserters allegedly loyal to self-exiled opposition leader Joshua Nkomo. The Army has killed hundreds of civilians in efforts to rout out the dissidents and their supporters.

The armed men killed Erick Stratford, 66, his wife Christine, 62, and two granddaughters, aged 15 and 12, after first parading them before their workers and asking if they were good employers. Two workers, who were often late on the job, denounced the Stratfords, the government spokesman said. The four were then taken into the house and shot to death with Stratford's revolver.

Jim Sinclair, president of the Commercial Farmers' Union, said he was "horrified" at the killings and would seek meetings with government officials to take steps to increase the security of the farmers. The incident brings to about 40 the number of whites killed by dissidents during the past year of violence in Matabeleland. The dissidents are believed to be responsible for a total of about 125 deaths.

After a series of incidents last year farmers appealed to Prime Minister Robert Mugabe for better security. Early this year, the farmers were issued with Army weapons. Mugabe then sent a North Korean-trained brigade of 5,000 troops into the area in January to put down the violence.

White farmers interviewed last month said they feared that they would be targets of the dissidents once the Army offensive ended.