"I pride myself on never having paid a bribe," said the old-timer, a European woman who has lived here for a decade and has learned the ways of the bureacracy -- utterly baffling and often costly lessons for any newcomer.

Her wallet is filled with cards of important people, infinitely more valuable in some cases than any amount of money she could carry. For a recently arrived visitor she gives this advice:

"Take one of your own cards," a necessary item in Mexico, "and write the name of this high police official on the back, then put his phone number under it with linea directa scrawled after it. If all else fails when a traffic policeman stops you, show him the card and ask him to call this man. He won't want to bother him. Don't confront the policeman. Then it becomes a macho thing. Just tell him this man will 'explain' everything.

"If worse comes to worse, tell the policeman you'll go to the station with him.He doesn't want to go because he'll lose money he could be getting in bribes. You have to remember, you are in the right no matter what you've done."

In this little lesson on how to deal with police (known as mordelones from the Mexican slang for bribe) are the keys to dealing with official Mexico at any level and a hint of why the U.S. government often finds itself at odds with Mexican officialdom. These rules, it should be noted, are easier to describe than to master.

First of all, one should make an effort to know personally as many influential people as possible (those business cards again). Personal relationships are almost everything. In a nation of big families, a kind of chain reaction may occur, so that after a while you will know at least a cousin of anybody you may ever need.

Those without such connections find themselves doomed to the purgatory of endless hours unattended in the inevitable waiting rooms.

There is a reciprocal aspect is this. If you can call on your friends with ease, they expect to be able to do the same with you, and on the diplomatic level this means mutual accessibility. A friend, once ignored or slighted, can easily become an enemy and the Mexicans have long memories of the days -- before oil -- when they often felt ignored or slighted by the United States.

WHICH BRING UP the second vital aspect of getting along either in or with Mexico -- what the French, whose culture the Mexicans have always envied slightly, call politesse.

Despite all the talk of machismo, or perhaps because of it, confrontation is not an accepted mode of getting along in Mexican society. There is an almost oriental obsession with saving face and the fastest way to reach a dead end in any kind of negotiation is to force an issue.

The painfully protracted U.S.-Mexican negotiations last year on the price of natural gas were largely a result of the confrontational approach attributed to the U.S. Department of Energy.

Mexican pride is such, however, that any suggestion it may be sullied is enough to lead to protracted problems. Even when the United States is wise enough to ask, rather than demand, something or its southern neighbor, Mexicans opposed for whatever reason to a given policy may make it seem as if adopting it would be giving in to Washington. This often invokes the principles that if Washington wants it, Mexico doesn't.

Oil has complicated matters by leading to the suspicion here than anything the United States does that seems to benefit Mexico is merely a tactic to get more petroleum.

All this may lead to infinite subtleties in communication and face-saving, an elaborate minuet of social and business intercourse that sometimes takes curiously clumsy turns.

The new U.S. ambassador. Julian Nava, made an effort upon arrival to speak Spanish as a matter of courtesy to the Mexican officials he encountered. A Mexican American scholar, Nava has no problem with the language, unlike many of his predecessors.

On meeting Mexican Foreign Minister Jorg Castaneda, Nava greeted him in the language of Mexico. Castaneda replied in English. Neither man would explicitly make an issue of this, but it created the curious situation of the U.S. ambassador speaking Spanish to a Mexican foreign minister replying in English.

THE FINAL REQUISITE for survival in Mexico is patience. What may seem the simplest thing can take a semingly interminable time to accomplish. This may be true even for those who have the proper contacts and manners.

A travel agency here, for instance, nearly went broke earlier in the year after allowing a government agency to charge $130,000 worth of tickets. Eight months later, almost $90,000 of the bill remains unpaid. The business was obtained originally through a mutual friend of the travel agent and the head of the government bureau. The friend's child is the god-daughter of the official. Even a plea from the godchild has not been able to pry the money loose.

As noted earlier, these rules of connections, politese and patience than to follow. It is not uncommon to see the newly arrived kicking the fenders of cars turning almost through them as they cross streets, learning Spanish epithets before they learn to order meals, and developing a level of hostility toward Mexicans that assures confrontation at the slightest provocation.

The last resort, of course, is bribery. A lot of it goes on. But while a little cash in the right hand at the right time may make life easier for a resident -- and may not, because the passing of money is an art few foreigners master with grace and the requisite style -- it is virtually useless on the diplomatic level. Even in a figurative sense it would be difficult for the United States to grease the palm of one of the world's greatest oil producers.

As Mexico grows more powerful economically and politically more influential among the nonaligned nations, Washington can expect to deal with Mexicans on their own terms. If it masters the game it may discover, like those who have lived here long enough to learn the ropes, that "anything is possible."