Travelers will love the euro - the new single European currency - which officially came into being on May 1. They'll no longer have to figure out how many zillion lire to the dollar or pesetas to the French franc or Deutsche marks to the guilder - plus they'll save a fortune not having to change money back and forth.

And one currency will make European price comparisons much easier. The fact that a 1.5-liter bottle of Coca-Cola might cost 3.02 marks or 6.50 francs is baffling. But from Jan. 1 - the start of a three-year transition period - double price lists will show French Coke costing, say, 98 euro-cents compared with 1.30 euros in Germany.During this transition, the rates of exchange between the euro and the particular currency of each nation that uses it will be irrevocably fixed, so there will not be a daily euro-franc exchange rate, for example, to worry about. Consumer organizations will publish price comparisons of popular items in the 11 countries of the euro zone. And it will be much easier to shop for the best cross-border air fares, hotel rates and other travel services in different countries.

The coming of the euro has been hailed as momentous, creating the largest currency union in financial history, with the euro rivaling the dollar and the yen on the money markets. But until January, when the euro starts to be traded, travelers will notice little change.

Even then, the only difference travelers are likely to see is that shops, restaurants and hotels may display their prices in euros as well as the local currency. With euro notes and coins not due to enter circulation for another three years, transactions in euros may seem unreal: an invisible currency that everyone is talking about and more and more people are using - even the British, whose self-imposed exclusion from the euro means that they won't join the European Monetary Union (the agreement that created the euro) until at least 2002.

But travelers should start thinking euros right from the start, and make as many transactions as possible in euros when this becomes possible next year. If you have problems figuring it all out, take heart. You can be sure that many Europeans are just as confused. And as Groucho might have said: "If you play your cards right, you can keep it that way."

A Frenchman I know still believes that one franc will equal one euro and that prices will therefore be the same across Europe. Otherwise, what's the point? he says. He may well have a point, but that's another story. The euro is a political project, designed to propel the nations of Western Europe toward political union. Creating the euro is one thing, but success is not guaranteed.

Europe seems to do many things in stages: Airline deregulation was finally achieved on April 1, 1997, after a series of reforms that started in 1987. The European Monetary Union will take a mere four years.

The countdown for the euro began in May 1998 when European Union finance ministers met in Brussels to agree upon the 11 countries - France, Belgium, Germany, Luxembourg, the Netherlands, Ireland, Austria, Portugal, Spain, Italy and Finland - which will participate in the "first wave" of the single currency on Jan. 1. The four European Union members who are not joining right away are Britain, Sweden, Denmark and Greece. Britain, Denmark and Sweden may join the second wave around 2002, while Greece (unlike most other countries) has not yet been able to fudge the tough limits on debt levels, inflation and interest rates - the "convergence criteria" set by the European Union.

On Jan. 1, the euro will become the official currency of the 11 participating countries - although not in the form of cash. National currencies will still exist alongside the euro, which can be used in noncash transactions, such as credit card payments, checks and direct debits. Countries not using the single currency, like Britain, Denmark, Sweden and Greece, will continue to experience exchange-rate fluctuations against the euro.

It's worth stating the obvious that there will be no exchange-rate cost between, say, the euro and the French franc, because it is not a foreign currency transaction, simply an "expression" of the same money. It is the official exchange rate that has to be used (something to watch out for with rogue traders).

On Jan. 1, 2002, euro notes and coins will be introduced and all prices will be posted in euros. National currencies will gradually be withdrawn and will cease to be legal tender by June 30, 2002, at the latest.

When they arrive in 2002, not all euro notes and coins will look the same. (You didn't expect it to be that simple, did you?) One face will be the same for all euro countries; the other side will bear suitable motifs to salvage national sentiments in a brave united Europe. There will be eight coins - 1- and 2-euro pieces and 1, 2, 5, 10, 20 and 50 euro-cents; notes will be in 5, 10, 20, 50, 100, 200 and 500 euros - different colors, but all the same size, like United States bills. The decision to issue the 500-denomination notes was made to placate Germany, which issues notes up to a face value of 1,000 marks.

At a euro-dollar exchange rate of 1.10, the new 500 euro note will correspond to $550 - a rival to United States bills as the underworld's currency of choice. Instead of lugging thick wads of $100 bills in a suitcase, you will be able to pack $1 million worth of 500-euro notes into a purse.

Meanwhile, a little less than four months away from the euro, double pricing is appearing in banks and shops across Europe. Banks and retailers are giving away euro pocket calculators to convert back and forth with the local currency.

Travelers should start collecting them to become familiar with the rates and to compare prices - and therefore the euro value of goods and services in different countries. Even in Britain - perhaps especially in Britain - where sterling will still reign, major retailers will accept euros, and major businesses are starting to denominate contracts in euros, forcing smaller suppliers to do the same.

During the three-year transition period, there will be no obligation for merchants to accept euros and no compulsion for you to pay in euros.

"Travelers will be able to pay for tickets in euros or local currency right from the start," says Anita Macleod, head of a euro task force at the International Air Transport Association in Geneva. "We will have common ticket stock available that accepts the euro or local currency - but we're not forcing airlines to deal in euros."

Henri Ruff, head of euro at Visa International in London, said: "The euro is going to make prices much more competitive across borders. Americans will find it easier to shop for holidays and trips across Europe because they'll be able to compare prices in euros. This transparency, this ability to compare, will influence the market and perhaps bring prices more in line across borders."

The Swiss and Norwegians are well prepared for the euro, he said, with hotels and restaurants ready to accept it as a foreign currency.

"We expect in the so-called front-line states in Eastern Europe - Poland, Hungary, Czech Republic, cities like Prague exposed to tourists - that hotels and stores will accept euros from Day 1," Ruff said, "in the same way that they might accept dollars or German marks now, leading possibly to unofficial - meaning more favorable - exchange rates."

"Our advice is to start dealing in euros wherever possible," he added. "We'll have euro traveler checks ready for Jan. 1. And start paying in euros wherever possible on your charge card."

Cardholders who want to pay in euros at places that are prepared to accept euros can do so, Ruff said, and they don't have to worry about whether their cards will work. "We expect card usage to increase, because it's the only way in the transition period for people to trade in euros," he said.

Travelers can expect wider swings in exchange rates between the dollar (or other currencies) and the euro.

"The euro itself will probably be a fairly volatile currency for a period of years," said William Essex, an investment consultant in London, "on the grounds that Germany is strong, Italy is weak, so they've got to settle which is dominant within the euro zone, whether Germany's strength is more influential on the currency than the peseta." He also said that a lot of currency traders are losing their jobs because of the euro, and that the ones who remain will be looking for something to do, so there will be greater volatility between the dollar and noneuro currencies.

Amanda Iremonger, European Monetary Union country program manager at Citibank International, in London, said:

"There is a huge amount of confusion. Europeans don't understand what's happening. If the Americans come in and know what's coming, then they'll be a step ahead."