More than 2 million voters cast their ballots by midafternoon today on the second day of voting in Rhodesia's black-majority elections.

With one day still to go, the figure surpassed by almost 200,000 the turnout in the five-day election last April, which was the first with black participation. Thus, the country's temporary British colonial administration was in a strong position to gain international acceptance for the election and the independent government that will be chosen.

The result is to be announced Tuesday.

The heavy turnout came in the face of increasingly bad weather and complaints by all three major parties of irregularities in the voting.

Last year, 1.87 million people voted in elections that put Bishop Abel Muzorewa in office as prime minister but failed to gain international recognition because it excluded several black guerrilla groups. The December peace agreement between the guerrillas and Muzorewa's government ended the seven-year civil war and restored the breakway colony to British colonial rule until the new government is elected.

Sir John Boynton, the British election commissioner supervising the voting, announced that as of 3 p.m. today the total vote was 2.028 million. He declined to give the voting percentage since no registration exists and it is becoming apparent that the country has considerably more voters than the estimated 2.9 million.

Rhodesia's population is generally estimated at about 7 million, including 200,000 whites, but no census has been taken since 1969 because of the bloody guerrilla war. It is suspected that the population is probably significantly larger since the country has one of the highest birthrates in the world.

Heavy rains caused rivers to swell and cut off some voters from the polls, but Boynton said special arrangements are being made to fly mobile polling stations to remote areas for the last day of the vote. Many flights for observers and the press to monitor the vote had to be canceled.

The protests about election procedures came from the parties headed by Muzorewa, who is backed by the white minority, and his two key rivals, guerrilla leaders Robert Mugabe and Joshua Nkomo.

Boynton called most of the charges absurd.

Muzorewa sent a letter to Lord Soames, the British governor, complaining that his supporters were being harassed and intimidated by Mugabe's followers in both urban and rural areas.

Edgar Tekere, the deputy leader of Mugabe's Marxist-oriented party, said, "The entire election is a nothing; it deserves no respect. There is massive, countrywide double-voting by Muzorewa's people."

Tekere and Nkomo's publicity director, Willie Musarurwa, charged that thousands of Muzorewa supporters were voting twice by using a mixture of Coca-Cola and paraffin to remove invisible ink from the hands of persons who have already voted.

The ink is applied to voters' hands before they get their ballots and is supposed to remain visible for several days under ultraviolet lights used in the polling booths to check for double voting. The procedure was devised to avoid voting fraud since no registrations list exists to allow the checking of names.

Boynton denied the allegation, saying the method is used in many African nations. A demonstration by Mugabe's party failed to prove its contention.