Alfonsin's start

He has come on with a swift determination unprecedented in recent Argentine history. In his first three weeks in office, Raul Alfonsin has tackled the military, then the unions, and now the economy in what one Buenos Aires daily calls ''our one last chance to get out of the mess we are in.'' There is an obvious euphoria in Argentina over the nation's return to democracy. But the tasks before Dr. Alfonsin are immense. He has wisely warned Argentines ''not to expect overnight solutions.''

Yet fast action is needed on a wide range of problems. The military's penchant for power must be curbed. For more than 50 years, it has repeatedly and arrogantly grabbed authority. In hopes of forestalling any future military action, Dr. Alfonsin swiftly retired most of the top-heavy corps of generals and admirals. He put curbs on military spending. He signed a law overturning the prior military government's amnesty decree of generals and police. And his government is seeking prosecution of many former officials for human rights violations during the past decade. Whether all this will keep the military from snuffing out his five-year presidential term, as it has all but one presidency during the past 50 years, remains to be seen.

Alfonsin has attacked the labor unions with equal vigor. He has proposed a union reform law that calls for immediate elections throughout Argentina's powerful network of labor unions from the lower levels up. The elections would be supervised by Argentina's electoral courts and are aimed at putting democracy to work in the unions. The plan would sharply curtail union power, and particularly the virtually unlimited power of labor leaders. Union officials are infuriated by the law and its implications. But Dr. Alfonsin has the support of Congress on the measure and the rank and file of labor appears to go along with it.

Ahead: The new President plans to take on the church and promote social reform.

Meanwhile, straightening out the Argentine economy would be challenge enough. With inflation at 1,000 percent a year, a $40 billion foreign debt, and virtual economic chaos, there are no easy answers. Dr. Alfonsin has imposed price and wage controls and import restrictions. ''Austerity and sacrifice are the keynotes,'' his new economics minister says. But Argentines are not accustomed to living with either.

The new President must convince the Argentine people to accept a period of austerity. If he can do that, he may well get the Argentine nation back on an economic track that will allow it to fulfill its potential as one of the world's richest lands.