Thorbjorn Falldin, a sheep farmer who ended 44 years of Social Democratic rule, resigned last night as premier of Sweden.

Faldin was brought down on the very issue he rode to high office - nuclear power.

His Center Party deputies repudiated a compromise Falldin had struck with their coalition partners over turning on two more nuclear plants. That left the craggy-faced premier no choice but to get out.

Political leaders in Stockholm will gather today to decide what to do next. The chances are that Falldin will be succeeded by one of his former coalition colleagues, Ola Ullsten, the 47-year-old leader of the Liberals.

Ullsten is expected to form a minority government with the Conservative, the third member of the team that drove Olof Palme and the Social Democrats from office two years ago.

A Liberal Conservative Government would play a caretaker role. Sweden must hold new elections a year from now. Palme might bring down a minority government at once. But he has told friends he does not want this because two elections in one year would not sit well with Swedish voters.

Palme can afford to be patient. The disarray among his "bourgeois" opponents is so great, he can look forward to an easy victory in 1979. Swedish polls now show Palme's party is well ahead of the other three combined.

In Stockhom at a press conference announcing his resignation last night. Falldin, 52, looked relieved rather than depressed. He had been forced into one compromise after another over the nuclear issue and his reputation as Sweden's "Honest Abe" was badly damaged. Before the reporters, Falldin sounded like a man who had barely escaped with his honor intact.

He said that there must be "give and take" in any coalition, "but no party can be asked to kill its own soul."

The "bourgeois" coalition was hopelessly split over atomic power from the day it won office in 1976. Falldin had campaigned vigorously against switching on any more plants and even promised to shut off the five in operation. The radiation dangers he claimed, were too great.

But his Conservative and Liberal partners, like Palme and the Social Democrats, were for a substantial increase in atomic power to free Sweden from foreign oil and fuel the industry that has given Sweden the world's second highest income after the United States.

In almost his first act in office, Falldin turned on plant number six. The crunch came a few weeks ago with the completion of plants seven and eight.

Falldin thought of resigning then, but made one more stab at holding on. He got his partners to agree to put off the operation of the two new plants until Sweden's nuclear agency pronounced that a safe place had been found to dispose of the atomic waste. Jubilant Conservatives declared they had won 99 percent of their battle for still more nuclear power.

That was too much for Falldin's Center deputies and his energy minister in particular. They insisted that Falldin win fresh concessions and, when he could not, he resigned.

There is a rough justice in this, according to Swedish observers. Falldin got to be prime minister because his party, with 86 of 349 seats in parliament, is the largest of the three coalition groupings.

There are few substantial policy differences between the Social Democrats and the "bourgeois" parties, apart from Falldin's nuclear stance. Almost everybody in Sweden enjoys their rich, welfare-capitalist state. Palme lost chiefly because the Sweden got tired of the same party in power for nearly half a century and concluded there was little risk of change with the opposition.