(FORTUNE Magazine) – Since the Year 2000 problem came to light, doomsayers have offered up plenty of frightening scenarios: planes falling from the sky, elevators hurtling people to their deaths, banks losing everyone's money. But despite the fact that many companies--as well as all levels of government--have scrambled to avert disaster, the panic is far from over. Only now, many companies aren't worrying about their own Y2K problems--they're worrying about something more vexing: other people's Y2K problems.

Most multinationals have spent vast sums of money fixing and testing their own systems, only to start wondering, "What happens if my customers in Asia are afflicted with Y2K problems and can't buy my products? Or what if all those ball-bearing factories in Brazil seize up and I can't finish my manufacturing?" Such concerns may not spell the end of civilization, but they could, at the very least, make for a really ugly first quarter.

The British and Dutch consumer goods company Unilever, for instance, finished its debugging this year and had set aside next year to test its most crucial systems. It was probably feeling pretty Y2K smug, until a poll revealed that 25% of its roughly 80,000 suppliers worldwide had yet to do anything on Y2K. "Other businesses, particularly medium and small ones, have woken up to it very late," says Unilever chairman Niall FitzGerald. "And even if they're fully alert to it now, the time left to them to get their systems compliant is not enough." So the company recently announced it would cut off any supplier who was not fully Y2K compliant by the second quarter of 1999.

Other companies are taking similarly drastic steps: The Dutch airline KLM, for instance, recently said it might cancel all flights on and around Dec. 31, 1999. KLM says its own systems are fine, but feels that certain European air traffic control systems and airports are unprepared and could cause schedule delays and safety hazards. "There are eight air traffic control systems involved in a flight from Amsterdam to Athens, and no one is claiming end-to-end responsibility," KLM's CIO Max Rens told a Y2K conference in London. "We don't trust the governments. We think they are too late." KLM is the only airline to panic publicly, but all airlines are crafting plans to address the worst-case scenarios.

Meanwhile some companies are just bailing out completely: Lou Marcoccio, the Y2K research director for the Gartner Group, tells of an American heavy-equipment manufacturer that determined that 40% of a major product line's customers were in the six Asian countries with the highest Y2K vulnerability. So the company is yanking the line from those countries and shifting sales to Western Europe and Mexico, where it sees lower risk.

Of course, on Jan. 1, 2000, it may turn out that Unilever, KLM, and others have spent millions for nothing; that the fear--and the cost--grew from assumptions that never came to pass. Knowing they may be throwing money away is frustrating enough, but many companies are also discovering that suppliers and customers are being less than candid about their Y2K readiness--a function both of mounting paranoia about possible legal liabilities and a general reluctance to fess up until they're obliged to. After all, why panic your suppliers and customers if all the year 2000 will bring is a wicked hangover?

With the lack of reliable information, the general confusion about the computer error's potential effects, and the fact that it's all but impossible to account for every link in the supply chain, Y2K is shaping up to be as frustrating a puzzle as most companies have ever had to solve. And their solutions to it will come with some serious implications. Visa International, for instance, is busily drafting fallback systems for authorizing credit card transactions in the event that phone systems collapse in countries like Thailand and Brazil--an outcome Visa considers likely. But ask David Starr, CIO of Knight Ridder and outspoken anti-alarmist, whether he thinks anyone should worry about the Thai and Brazilian phone systems crashing, and he'll tell you, "No way. That's ridiculous." One of them is wrong, and will pay dearly. The question now is, which one?

--Melanie Warner