Fifty-nine persons, most of them tourists, were killed today when a Rhodesian airliner crashed only minutes after taking off from a holiday resort in northern Rhodesia where a similar plane was shot down by antigovernment guerrillas last September.

Military and airport sources said it appeared that the plane, a four-engine Viscount, was hit by a ground-to-air missile, which the guerrillas are known to have.

Last September's attack was followed by a sharp escalation in the six-year-old war with Rhodesian forces carrying out devastating air and ground raids on guerrilla sites in neighboring Zambia for the first time.

The plane that crashed today was one of two Air Rhodesia aircraft to leave Kariba Lake within a 15-minute period. The second, whose passengers included Rhodesia's defense chief, Lt. Gen. Peter Walls reached Salisbury without incident.

A terse announcement from the state-run Air Rhodesia tonight said simply that the first flight from Kariba Lake to Salisbury, the Rhodesian capital, had crashed shortly after its 5 p.m. takeoff and that there were no survivors.

An airline spokesman said Rhodesian security forces had reached the plane, which went down in thick bush near the border with Zambia. The area is infiltrated by guerrillas of the Zimbabwe Peoples' Revolutionary Army led by Joshua Nkomo.

Capt. Pat Travers, general manager of Air Rhodesia, said a distress call was received from the stricken Viscount before it crashed. He did not say what the crew said.

Nkomo claimed responsibility for the Sept. 3 downing of an Air Rhodesia Viscount by a SAM 7, alleging that it was carrying military equipment. At the time, Nkomo warned that his forces would continue to shoot down Air Rhodesia aircraft if the guerrillas thought they carried military supplies.

The downing of the Rhodesian aircraft last September by the Soviet-backed guerrilla forces cost the lives of 48 people. Thirty-eight were killed in the crash and 10 survivors were shot by guerrillas who came upon the scene of the crash.

That incident worsened the conflict between Salisbury's biracial transitional government and the black nationalist guerrillas and put an end to preliminary peace talks that were going on between Nkomo and Prime Minister Ian Smith.

Rhodesian security forces reacted to the September crash by launching raids on Nkomo's guerrilla camps in neighboring Zambia, causing hundreds of deaths and a further deterioration in prospects for a negotiated settlement to the war, now entering its seventh year.

If it is confirmed that today's crash also was caused by guerrilla fire, a similar response from the Rhodesian forces is considered likely, although they are seriously short of manpower and are preparing for a full-scale mobilization at the time of elections for an independent black government April 20. Nkomo, along with his guerrilla partner, Robert Mugabe, have threatened to disrupt the elections.

Reports from Sailsbury tonight said the stricken plane sent out a distress signal six minutes after taking off from Kariba lake, a popular holiday spot with Rhodesians, with a casino and excellent fishing.

A Rhodesian Air Force spotter plane immediately went out to search for the Viscount and found the burning wreckage a short time later, an airport spokesman said.

Among the five dead crew members in today's crash was a black trainee air hostess, Regina Chigwada, 23. Chigwada had been in training since Feb. 8 and was set to become Air Rhodesia's fourth black hostess in what had been an all-white in-flight personnel.

In anticipation of a black majority government, the Salisbury government has been training blacks for positions in its civil service, to which they were denied access in the past by racial barriers.

Associated Press correspondent Maureen Johnson, who was aboard the Air Rhodesia plane that took off 15 minutes after the plane that crashed, reported from Salisbury :

The second flight, instead of swinging left, as had the ill-fated plane, circled for almost 20 minutes over the giant Kariba Lake, on the tense border between Rhodesia and Zambia.

Air Rhodesia officials have taken extraordinary security measures since the September crash. On short, domestic flights, the airline's pilots fly unusually low to make their planes more difficult targets to hit. On longer flights to neighboring South Africa in which big Boeing jetliners are used, Air Rhodesia pilots aim for maximum altitude.

Arrival and takeoff times are varied and routes are often changed from one flight to another. At night, interior lights are switched off and passengers must pull down their window shades.