Mexico announced tonight that it will drop most exchange controls on the peso as a major step in what new President Miguel de la Madrid called a "rationalizing" of the economy.

Private financial analysts here estimated that the free-floating peso would plunge to a rate of well over 100 to the dollar. The basic fixed rate until tonight was 70 per dollar, while the black-market rate exceeded 120.

In an address this evening by newly reinstated Central Bank director Miguel Mancera, the administration said that two foreign exchange markets would go into effect as of Dec. 20, "one subject to control and the other completely free."

The new system, together with revisions in interest rates, is designed to attract desperately needed foreign exchange and to replace an attempt at rigidly fixed exchange rates put into effect Sept. 1 by then-president Jose Lopez Portillo.

Violation of those controls was described by Mancera as "massive, extending the corruption" that has plagued Mexico.

A special, or preferential exchange rate will be set to subsidize a few essential imports, expenditures by special border industries, payments on loans contracted in foreign exchange and expenses related to the diplomatic corps. Mancera said that it would not be "prudent" to drop all controls immediately but indicated that the goal is eventually to bring the preferential and free rates together.

In the first 10 days of his six-year term, de la Madrid has taken what he called "drastic but inevitable" steps to reorder an economy wracked by nearly 100 percent inflation, high unemployment, zero or negative growth, "paralyzed" investment and an external debt of $83 billion.

Most of de la Madrid's intended solutions for the crisis are in line with conventional, relatively conservative economic thinking of the kind promoted by the International Monetary Fund. Mexico is committed to reduce the government budget deficit under an agreement reached with the IMF before de la Madrid took office.

In essence, the new president is raising taxes and charges for government services while phasing out many subsidies. Price controls have been dropped from thousands of items and preserved on only a few hundred "essentials." The price of gasoline was doubled for the second time in four months.

"You don't measure an administration on its first 10 days," said one diplomat with long experience here, "but he has moved pretty decisively, not only on economic things but with some pretty effective cage-rattling on the political side, too."

In his speeches, his decrees and the laws he has proposed to Congress, de la Madrid has set about undoing the work of his predecessor Lopez Portillo. The previous president's last year in office was marked by moves seeking mass political support that increasingly left the economy crippled.

In his last state-of-the-nation address on Sept. 1, Lopez Portillo nationalized all private Mexican banks and imposed strict exchange controls as the peso slid steadily below one U.S. cent in value. He then proceeded to hold massive rallies around the nation and received ringing endorsements from Mexico's leftists.

De la Madrid has said repeatedly that there will be no reversal of the bank nationalization. In his inaugural address, in other speeches and in meetings with various influential groups, however, he has left open the possibility that a substantial interest in the banks will be returned to private, albeit diversified, ownership.

In his budget address to the Congress earlier this week, he dismissed what he called "populist window dressing" and repeatedly emphasized "the decision of the federal executive to confront the crisis from the standpoint of truth and realism."

Although the proposed 7 trillion peso budget for 1983 appears almost twice as high as this year's, even the conservative business daily El Financiero estimates that in inflation-adjusted terms this represents a 15 percent decline.

In accord with a letter of intent signed with the IMF shortly before de la Madrid took office on Dec. 1, this government will have to reduce its budget deficit from an estimated 16.5 percent of gross domestic product this year to 8.5 percent in 1983 and 3.5 percent in 1985. About $3.84 billion in IMF funding rides on reaching those goals.

The political costs are also impossible to foresee, but the powerful labor movement allied to the ruling party is restive.

"The workers will not just sit with their arms folded. We shall act," Fidel Velasquez, the aging leader of the Labor Congress and patriarch of Mexico's unions, told local reporters.

Mexico has no government unemployment or welfare system, and has depended on keeping prices down, artificially if necessary, to satisfy the basic needs of its people.

De la Madrid proposes to cushion the hardships of the poor by using highly selective public works programs, increased government efficiency, reduced corruption and especially fiscal incentives for investment and development in some of the hardest hit rural and urban areas.

Bank director Mancera said the rigid two-tiered system adopted by Lopez Portillo -- with 50 pesos the preferential rate and 70 the ordinary rate -- resulted in losses of 100 billion pesos to the banking system to support the peso.

The earlier system not only failed to attract foreign exchange and stop the flight of dollars but also provoked flight of pesos. These were exchanged near the border with the United States, where yet another legal rate had gone into effect, or across the border, where the free rate was even higher.