The Latin American economy as a whole grew by 6 1/2 percent in 1979, despite inflation running at 51 percent and severe constraints imposed partly by the cost of oil imports.

Executive Secretary Enrique Iglesias of the U.N. Economic Commission for Latin America (ECLA), offering this statistical profile in a year-end news conference, noted that the growth rate climbed from 4.2 percent in 1978 in the face of "a far less favorable world situation."

Iglesias stressed that the three largest economies, Argentina, a newly dynamic Mexico and Brazil, accounted for high overall growth, and he listed plenty of problems to condition the optimism.

Nevertheless, the performance underlined how far and fast the region has come:

Not quite 20 years after the U.S. initiated Alliance for Progress effort in massive economic aid set an elusive goal of 2 1/2 percent growth annually in the area's gross national product, that pace was nearly doubled last year. (Because population growth in the region is 2 1/2 percent annually, the per capita growth was 4 percent.) This came at a time when U.S. aid to Latin America has fallen to the point that repayments on loans made in the 1960s now nearly offset new assistance.

The hemisphere, once said to catch pneumonia when the U.S. economy sneezed, has proven capable of expansion despite American stagnation and recession.

After a decade in which Brazil was the solitary engine of consistent high economic performance among the larger regional countries, Mexico -- blessed with oil -- bids to outpull its own weight. It may be just in time. Brazil, almost without oil, now is contributing as much to the area's indebtedness as to its growth.

Mexico's prospects of broad growth already is having an impact on the United States, far beyond the highly publized, sometimes rancourous negotiations that produced a natural gas purchase agreement in September.

Assistant Secretary of Commerce Julius Katz said in a recent speech that U.S. exports to Mexico, worth $6.7 billion in 1978, were rising by 50 percent last year. U.S. exports of Mexican goods, not yet including much oil, are increasing almost apace.

"I expect in the next few years to see Mexico realizing a surplus in its trade accounts with the rest of the world," Katz said. U.S. purchases of Mexican oil should make Mexico a net exporter to this country. "Mexico will undoubtedly move up from our fifth largest trading partner to perhaps second or third," according to Katz.

"As the economy grows, Mexico will be exporting more and more manufactured goods to the United States in addition to oil, gas and other raw materials, he said. In this trend, Mexico is typical of efforts throughout the region -- with Brazil again setting the pace through exports to U.S. and other competitive markets of manufactures from auto engines to light aircraft.

One of the dynamos in Mexico's current upsurge is the steel industry, which is growing by close to 10 percent annually,. Production of more than 7 million tons last year was insufficent to meet demand.

In the long run, though, Mexican decisions on the pace of exploitation of massive oil reserves will be the most crucial at home, to the United States and to the region.

Uruguayan economist Iglesias, who has directed the Economic Commission for Latin America through the decade, recently undertook a worldwide mission for U.N. Secretary General Kurt Waldheim to more than 20 oil-producing and -consuming nations.

In his press conference at ECLA headquarters in Santiago, Chile, Iglesias said price was just one aspect of the oil problem, which he defined as "fundamentally a crisis of a wasteful and shortsighted development style of industrialized countries." He added:

"This crisis also threatens developing countries, which lack the defenses of industrialized countries and must face up to severe structurul changes whose effect is already being felt in many countries in the region."

However, only Brazil demands oil on a large scale, with the other large countries in the region producing at least a large part of their own needs while Venezuela and now Mexico are major exporters.

Although Iglesias is said to have found little hope during his world tour for helping the smaller importers on price, he was struck by the feasibility of assuring them of supplies and financing -- both often haphazard now.

Perhaps with this in mind, Iglesias proposed as a goal for the '80s "to strengthen regional cooperation both in its formal aspects and in the new forms of Latin American integration."

In fact, efforts long encouraged by the ECLA to create common markets in the region largely have foundered, although the sought-after trade expansion has occurred ad hoc in particular products.

Iglesias' figures on economic performance are preliminary but have proved in the past to be highly accurate. They show Argentina's inflation, now at 158 percent, persisting along with an improved growth rate. Brazil's inflation rose to 65 percent from 38 percent in 1978.

Accordingly, Iglesias described "inflation and the social requisites of stabilization policies" as major challenges facing the region, along with consolidation of growth.

"The expansion achieved by the majority of less developed countries of the region was considerably slower and less satisfactory and was of little benefit to some of the poorest sectors of the populations," he said.

In overall trade, ECLA figures show that Latin America ran a deficit on current account of $20 billion due toa sharp increase in debt service payments and remittances of profits. This was offset by an inflow of capital that produced an overall surplus of $3.5 billion in the balance of payments.

Brazil, already heavily in debt and hit by outlays for oil, swung from a surplus of $4.6 billion in 1978 to a deficit of $2.5 billion.