A second year of recession during 1982 shoved Latin America's developing countries into their worst economic troubles in nearly half a century, crippling development plans, leaving millions unemployed and threatening to trigger a disastrous series of financial collapses.

After a dismal year of stagnation or falling production in 1981, continuing declines in values of export products, high inflation and staggering foreign debt obligations carried many Latin countries from recession to crisis. At the end of 1982, several of the region's economies remained afloat only through special international aid packages or drastic emergency measures by troubled governments.

The region's three largest countries--Mexico, Argentina and Brazil--frightened the international banking system with the specter of default on their massive foreign debts and ended the year negotiating multibillion-dollar stabilization packages with the International Monetary Fund.

Many other countries faced similar, if not so dramatic, crunches. The Venezuelan and Colombian governments were forced to intervene in major commercial banks, and Chile and Uruguay suffered financial crises that ended in large currency devaluations. Bolivia found itself unable to meet its foreign payments obligations, and a new democratic government found the treasury empty when it took over in October. At least nine countries opened negotiations with the IMF for special aid.

Overall, the United Nations Economic Commission for Latin America estimated that the region's economies shrank nearly 1 percent in 1982, compared with 1981's modest growth, and that per-capita output fell more than 3 percent. The declining activity comes after a decade of average annual growth rates of 6 percent.

The U.N. commission reported that the region's average inflation rate was almost 80 percent in 1982. Rates ranged from a low of about 3 percent in Guatemala to more than 300 percent in Bolivia.

"In 1982, Latin America suffered its worst economic recession in the entire postwar period and probably the most serious since the worst years of the Great Depression," ECLA Executive Secretary Enrique Iglesias said in a year-end statement.

While the United States and most of the industrialized West suffered from stagnant growth and high unemployment, the effects of the recession in Latin America's dependent economies were far more severe. Chile, described by some experts as a model of health just two years ago, led the list of contracting economies with a 13 percent decline in output and an unemployment rate of 23 percent.

In other South American countries, estimates of unemployment--including the underemployed-- ranged as high as 45 percent.

In conflict-torn Central America, the gross product fell in all countries except Panama, according to ECLA. The economy of El Salvador contracted by 4.5 percent, after dropping by 20 percent in the previous two years in the midst of open guerrilla war.

Argentina, stricken by the disastrous Falkland Islands war with Britain, saw its economy decline almost 6 percent in the first nine months of the year, while real wages fell 13 percent and inflation approached 200 percent at year's end.

The country's central bank was forced to rearrange the terms of about $4.7 billion in foreign debts private firms were unable to pay--offering an ominous signal for banks with a stake in the more than a dozen Latin countries with oversized foreign debts.

By the end of the year, Latin America's total foreign debt was calculated in some surveys as close to $300 billion, and the problem of repayment had become one of the most pressing for Western economic leaders. The debt burdens forced harsh internal economic discipline not only in Mexico, Brazil and Argentina, but also in such poor countries as Bolivia.

As repayment obligations reached an estimated level of 60 percent of exports across the region, a number of leaders began to call for drastic measures by the industrialized nations and international organizations to restructure the debts and make repayments more manageable.

"Latin America can and wants to pay," Colombian President Belisario Betancur told President Reagan during the latter's trip through Latin America in December, "but when placed before the abyss of a brutal adjustment in its economy due to a lack of support from the financial world . . . it could see itself swept along by social forces to declare itself insolvent, producing reactions that no one desires."

The trigger for the crisis in many countries was the continuing recession in the industrial West and the consequent losses both in prices for exports and the relative terms of trade with industrial powers. A series of primary products crucial to Latin countries--including petroleum, metals and agricultural products--slumped on international markets, in some cases to their lowest level in 40 years.

Even though the Inter-American Development Bank estimated late in the year that overall exports would increase by almost 4 percent in 1982, when inflation was taken into account, the real value of exports dropped, and the cost of finished products imported by developing countries remained the same or increased.

The result for many countries in the region was a deepening internal stagnation. It became increasingly difficult to export enough to raise the sums needed to pay foreign obligations.

For many countries, an already bad financial situation was worsened by the troubles of Mexico, the first Latin giant to attract an international rescue operation. When Mexico suddenly postponed repayment on about $10 billion of its $80 billion foreign debt in August--leading the U.S. Federal Reserve and other central banks to organize more than $4 billion in special emergency credits--many private banks suddenly moved to lower their exposure around the region.

As a result, many other countries seeking financing to finish the year were nearly choked off. Brazil, which had until then managed to keep pace with obligations on its debt of close to $80 billion, found its sources of financing dried up in September. It balanced its foreign payments at the end of the year only with the help of a special $1.2 billion loan from the U.S. government.

In December, Brazil said it will need $9.6 billion in new and renegotiated loans from private banks to balance its foreign payments for 1983. It also expects to borrow $2.5 billion from the IMF.

Argentina, meanwhile, fell well behind on its own debt payments while negotiating a $2 billion loan package with the IMF, in addition to its unilateral rescheduling action on the $4.7 billion in private debt. Venezuela had trouble finding private banks to help it restructure its short-term debt at the end of the year, leading to a Cabinet crisis and a huge flight of capital from the country.

Most of these countries' governments were obliged to draw up austere economic plans in the effort at stabilization, including sharp sacrifices in some cases for both business and wage earners.

Brazil and Mexico, with inflation rates near 100 percent, pledged themselves to anti-inflationary policies, and both are expected to take steps to hold down salaries and cut back government spending.

Argentina's military government has made a similar commitment, saying the government's deficit will be cut to close to 2 percent of the gross national product in 1983 from its level of nearly 4 percent in l982 and pledging that any economic recovery will be limited to a 5 percent growth rate.

While government officials in these countries hope to see a return to modest economic growth this year, it's feared the stabilization measures will continue or deepen the recessions, even if a recovery begins in the United States and Europe.

For the rest of the region, improvement will remain dependent on a full recovery in the industrialized nations. Weak improvement in the developed world, economic analysts add, can only mean a continuation of the stagnation and crisis in Latin America.