Getting a telephone installed in Mexico can take years -- five, in some parts of the country. Once you get it, it will be a mixed blessing. There often is no dial tone. Calls travel over an antiquated, overloaded jungle of switches and wires and may get lost along the way. Although service is sparse, the telephone company is huge and unwieldy, employing more than 49,000 people nationally, who are represented by powerful labor unions.

Care to buy a piece of the system?

Today is the deadline to apply, and two U.S. regional telephone companies, Nynex Corp. and Southwestern Bell Corp., are on the list of hopefuls. They believe that by injecting capital and modern technology they can turn the system around and make it grow rapidly as Mexico reforms its economy.

"Telephone companies aren't that different worldwide," said Eugene LaBorne, a Nynex official who is involved in the Mexico bid. He conceded that risk exists but said that, in sum, it would be "a very sound investment."

The seven "Baby Bells" created by the 1984 breakup of the Bell Telephone System have been frustrated by the slow expansion of their solidly profitable core business of local phone service. Cash-rich, they are increasingly turning to overseas markets in search of growth. But they are finding, sometimes the hard way, that less developed parts of the world can bear little resemblance to the comfortable, prosperous perches they occupy at home.

"This is uncharted territory," said John S. Bain of the Florida-based securities firm Raymond, James & Associates. "They may lose their shirts, but they should try it {and} any opportunity for growth."

So far, the Bells have made a series of generally small ventures abroad in such fields as cable television, cellular phones and consulting. But now, jumbo deals are being dangled before them as governments all around the world are privatizing telephone companies in search of new technology and new ideas, as well as cash. To date, Baby Bells have done two large deals of this type, one swimmingly smooth, the other a failure and a possible signal of what lies ahead.

Bell Atlantic Corp. of Philadelphia, which owns the Washington area's Chesapeake & Potomac Telephone Cos., and Ameritech of Chicago paid $2.4 billion for New Zealand's phone system. But in Argentina, Bell Atlantic was part of a group that won a bid for half the country's system, and then lost it as it got caught in the middle of a nasty fight among rival politicians.

Analysts praise the Baby Bells for focusing on a business they know well, rather than trying to branch into new fields, as they have done in the United States with mixed success. For all the complaining Americans do about the fallout of the Bell System breakup, U.S. phone companies are still widely considered the best in the world.

But there is less confidence in their ability to navigate the often tempestuous world of business in developing countries, where corruption and inefficiency may be a way of life. The companies have made heavy use of consultants in foreign markets. But some analysts suggest that the telephone companies are walking on thin ice. "There's a huge educational job that still needs to be done at a senior level at these Bell companies," said one analyst who follows the companies.

For now, many of the Baby Bells remain bullish on the outside world and all eyes are on Mexico, which after long delay is taking to market a 20.4 percent stake in Telmex, the national telephone company. The stake consists of voting stock valued at about $1.4 billion and will give the buyers a controlling interest. The rules of the game, however, are that the party buying that stake must be Mexican-controlled.

This means foreign investors must team up as minority stake-holders with Mexican parties. Nynex and Bell Canada Enterprises have grouped with Casa de Bolsa Inverlat Associates, a Mexican investment house. Also in the running is Southwestern Bell Corp., with a different team. "Naturally we are interested," said Southwestern spokeswoman M. Annette Unser. "We share this 2,000-mile border, and working together would be mutually beneficial."

Two other U.S. companies, US Sprint Communications Co. and GTE Corp., have received initial clearance to bid but decline to say whether they will be doing so.

Whoever wins must commit to sinking at least $12 billion into the system over five years. They must agree to install modern equipment, increase the number of lines by 12 percent a year and begin whittling down the backlog of 1.2 million line orders.

"We have a few horror stories," conceded Carlos Casasus, Telmex chief financial officer.

In return, the owners will get pledges on what they can charge and, for six years, an almost airtight monopoly over all types of telecommunications, a situation the Baby Bells have long since kissed good-bye in the United States. Here they are barred from the long-distance and database business altogether and face competition in almost every facet of what they can provide -- pay phones, Yellow Pages and even, with large corporate customers, local telephone service.

Some analysts are nervous that the foreign investors will not have voting control over Telmex. But Nynex said it expects that it and Bell Canada will hold day-to-day operating control, although the Mexican partners will hold legal control. LaBorne said, "There is trust, and we believe in each other."

Resistance from Telmex's labor unions is also cited as a potential problem. Aware of their power, Nynex has taken the precaution of sending a former chairman, Bud Staley, to meet with labor leaders in Mexico City.

As with any company going abroad, the Bells face political risks. ITT, for instance, once owned the Chilean telephone company and saw it nationalized by President Salvador Allende. (It is now private again, owned by Telefonica of Spain.) Nynex expresses full confidence that Mexico's Carlos Salinas, now two years into a six-year term, will stick by his fast-developing agenda of liberalization.

For the time being, Nynex is focusing on the positive sides: Telmex is making money and is growing. "There are going to be 30 million people in Mexico City by the end of the century," LaBorne said. "The growth potential of this telephone company is enormous."

In contrast to all the early optimism on Mexico, the Argentina deal demonstrates many of the potential pitfalls of competing internationally. There, Bell Atlantic was teamed with a group led by Manufacturers Hanover Trust Co. seeking a 60 percent stake in the northern part of Argentina's debt-laden, money-losing state phone company, Entel.

Terms called for the buyers to pay $100 million cash and to arrange for the turn-in of about $2.3 billion in Argentine government foreign debt in exchange for an equity stake in the company. Such a "debt-for-equity swap" is a prime means by which developing countries reduce their debt burden.

Bell Atlantic agreed to manage the system in return for substantial fees and a 4.9 percent equity stake. It was a virtually risk-free arrangement, with the company committing none of its own capital.

The Argentine government initially selected its bid. Bell Atlantic dispatched a team of 50 to survey the system and get down to work. But when a deadline arrived for signature, Bell Atlantic's group had neither the financing nor a final agreement on terms with the Argentines.

Many analysts fault Manufacturers Hanover for overestimating the enthusiasm of other banks for taking Entel equity in place of Argentine debt. Others suggest that the bank had trouble assembling the $100 million cash portion of the deal. For its part, Bell Atlantic stuck by its refusal to put in any of its own money, having promised its shareholders at an annual meeting that it would not risk its own funds.

Bell Atlantic also ran afoul of Argentine politics, many people in Buenos Aires believe. Its bid had become tied to controversial politician Maria Julia Alsogaray, who was overseeing the privatization. When the deadline was not met, she suggested that Bell Atlantic be given more time; her political rivals worked hard to see that it was not, partly as a way to undermine her.

Argentina then gave the deal to a team that included two phone companies, Stet of Italy and France Telecom, and a bank, Morgan Guaranty Trust.

But in October, that group and the winner of the southern zone, which included the Spanish phone company Telefonica and Citibank, exercised their new-found leverage and demanded a renegotiation of rates they would be able to charge. The government, desperate to conclude the deal, made major concessions.

Bell Atlantic, however, has not accepted defeat, protesting to the Argentine government that the two new winners were offered better terms.

Bell Atlantic spokesman Michael Houghton said the company is confident of its prospects for some type of positive response.

"I think we'll be heard," he said, "because I think our case is very strong."

Correspondent Eugene Robinson contributed to this report from Buenos Aires.