More than a million Rhodesian blacks voted today in an overwhelming first-day turnout for elections that could sharply alter the politics of Southern Africa.

Despite rain in much of the country, long lines started forming hours before the polls opened in many areas and were 1 1/2 miles long by the late afternoon. No serious incidents were reported and the mood of the crowds was generally cheerful.

John Boynton, who heads the British commission supervising the election of a black-majority government to bring the war-torn country to legal independence, said the turnout by 3 p.m. was 886,482. That was 55 percent more than on the opening day of last year's election which was not recognized internationally although it was the first in which blacks were allowed to vote.

The midafternoon figure meant that by the end of the first of three days of voting more than 1 million of the estimated 2.9 million voters had gone to the polls, a figure that should boost British hopes that the election will gain world approval as being free, fair and representative.

The election, the culmination of a three-month return to colonial status for the breakaway nation, is designed to bring Rhodesia to legal independence under the African name Zimbabwe. International recognition would finally put to rest the 1965 unilateral declaration of independence by white Rhodesians to maintain white minority rule and it is expected to end Africa's bloodiest struggle against white domination.

Although the voting will end Friday night, ballots will not be counted until Monday and the results are not expected until Tuesday morning. The weekend will be spent moving ballot boxes from 657 polling stations, many of them remote, to eight provincial capitals for counting. The purpose is to avoid intimidation by making it impossible to tell how any district voted.

The only surprise on the first day of voting was the abrupt departure from the country of guerrilla leader Robert Mugabe for a visit to Mozambique and Tanzania. He is expected to return to Rhodesia Sunday after talks with Mozambican President Samora Machel and Tanzanian President Julius Nyerere, both sharp critics of Britain's temporary rule.

The spokesman for Lord Soames, the British governor, said the government was "surprised to learn of Mr. Mugabe's sudden departure."

With a touch of irritation in his voice, Nicholas Fenn, the spokesman, added: "The future of Zimbabwe is being determined here, not elsewhere. We shall do our best to prevent this unexpected development from slowing down the progress of recent days."

Indications of an easing of tensions between the warring sides continued as Gen. Peter Walls, head of the Rhodesian military, held a series of precedent-shattering meetings.

He met last night with Mugabe, who called the meeting "quite good." Mugabe's top military leader, Gen. Rex Nhongo said the two discussed integration of the Rhodesian security forces with the guerrilla armies.

Yesterday it was disclosed that Walls met last weekend in Maputo with senior Mozamblican officials, including Sebasteao Mabote, vice minister of defense. Mugabe said at an airport press conference today that the meeting was "very cordial" and a Mozambican source said Walls and Mabote embraced at the end of the session.

Walls refused to talk about any of the meetings.

A key indication of the improved relations, at least during the election period, between the Rhodesian military and the guerrilla armies of Joshua Nkomo and Mugabe emerged at today's cease-fire commission meeting.

The Rhodesian representatives on the joint commission to monitor the truce said that it would be a waste of time to investigate alleged breaches, "many of which related to incidents which took place a considerable time before and which were in some cases of a comparatively minor nature." Instead there was "much business to be discussed concerning positive measures on reconciliation and the creation of permanent peace," the military spokesman said.

In the past the Rhodesian military has been at pains to publicize every alleged breach by the guerrillas.

Both Mugabe and his main rival, former prime minister Abel Muzorewa, voted in Salisbury today while Nkomo visited constituencies in his tribal stronghold, Matebeleland.

Muzorewa arrived at the polling station in a black township of Salisbury in a helicopter. This prompted a complaint from Nkomo's second in command, Josiah Chinamano, that it was a campaign stunt.

In the countryside the election often seemed to be an excuse for a celebration. At the beer hall of Protected Village No. 5 in the Madziwa tribal trustland north of Salisbury the bartender put in an extra supply of chibuku, a sorghum-based beer. He predicted a record day and his expectations seemed to be coming true as hundreds of voters streamed from the polling station to buy one-quart jugs for about 40 cents.

Lloyd Bumke, 45, a teacher, said he felt the election was "very free" especially compared with last year where there was "a little bit of forcing" people to vote.

Hundreds of workers on farms north of Salisbury voted at mobile polling stations, which moved from farm to farm, protected by about half a dozen police and a contingent of 20 well-armed security forces.

One of the main attractions at the polls for voters was the presence of 571 unarmed British policemen, most wearing their famous helmets.

One of the policemen, from the Liverpool area, said, "I'm just a British Bobbie wandering around the bush and loving every second of it." He said he planned to sleep with the ballot boxes under his bed each night until they are collected.

Everyone, he said, wanted to try on his helmet. The word is that they will go up to $300 on the collector's market -- if anyone can manage to lay a hand on one.