In Japan and Scandinavia, market penetration is so high that only the very young and very old tend to go without. In Italy and Britain, the rapid growth in subscriptions means mobiles are ubiquitous among adults; and other large European markets are not far behind.

In Ireland, Christmas proved to be a boom period for the sales of mobile phones, with Eircell reporting that it had sold 200,000 units. Esat Digifone is also said to have had strong sales, suggesting that around 300,000 units were sold between both operators. This would also suggest that mobile phone penetration is now more than 60 per cent.

Only in the developing world and the US - where local factors retarded growth - is the use of wireless, or "cellular", handsets still comparatively rare.

Few technologies have been embraced so quickly: more than 700 million handsets have been sold in less than a decade. But there is growing evidence that the years of breakneck expansion may be coming to an end precisely when the industry can least afford it.

Operators have committed more than £200 billion sterling (€255 billion) in Europe alone for investment in third-generation networks. To pay for this, more than half a dozen companies are hoping to raise money from the already depressed equity markets.

NTT DoCoMo of Japan and Orange, the mobile arm of France Telecom, will be the first to test the water next month and are currently trying to persuade investors to buy shares worth an estimated $15 billion (€15.9 billion) between them. Fears that the industry may be reaching saturation point are the last thing potential investors want to hear.

The trigger for this latest pessimism was a disappointing set of sales figures from Nokia, the world's largest handset manufacturer. Coming from anyone else, the numbers would have been cause for celebration. Nokia sold 128 million handsets in 2000 and estimated the total world market at 405 million - up 45 per cent on 1999.

Yet analysts were hoping for something even better. Consensus estimates were for Nokia to sell 135 million and the total market to reach at least 420 million. Even though Nokia itself had previously suggested that the market might "exceed 400 million", its end-of-year figures were instantly interpreted as evidence of a slowdown in the critical pre-Christmas sales period.

Until now, Nokia had been the sole survivor of the increasingly competitive handset price wars. Ericsson and Motorola have both issued profit warnings, and the merest hint of weakness from Finland was enough to knock 18 per cent off Nokia's share price.

The results were leapt upon by the bear market's growing crowd of doomsayers. According to Per Lindberg, an analyst at Dresdner Kleinwort Wasserstein, the figures prove that even Nokia cannot avoid a slowdown in sales as market penetration approaches saturation point. "Now the market will understand that even the strongest ship will eventually sink and Nokia is not immune from the weak market conditions," he says.

Other commentators are unsure whether to read the news as proof of market weakness or just a surprising admission of problems from its biggest supplier. But neither interpretation is helpful for the Orange and DoCoMo bankers trying to convince investors of stable demand growth.

Wireless operators and manufacturers prefer to look beyond simple subscriber numbers. They hope improvements in technology and changing handset fashions will encourage growing numbers of existing users to upgrade their handsets to newer models.

Mr Peter Richardson, principal analyst at Dataquest, typifies this more optimistic view. "If you look at the replacement market for televisions or VCRs, you have life cycles of 10 years. For a mobile phone it is probably on average about two years, and about 1.5 in western Europe and nine months in Japan."

Replacements for existing handsets already represent 40 to 50 per cent of Nokia's global sales and the company has been working to transform many of its models into fashion accessories for younger consumers.

The danger here is that the replacement market is highly vulnerable to wider economic conditions. Fashion accessories do not sell well in a recession, and signs of a slowdown in the US - still the world's largest mobile market - may have played a big part in the disappointing end-of-year sales figures.

Health scares are another worry for manufacturers. The scientific evidence of any harm caused by handset radiation remains scant. The worst that critics can say is that no one can prove that mobile phones (or their radio masts) are absolutely safe.

But consumer attitudes are another matter. Public opinion may have been influenced by memories of similar assurances about the risks of "mad cow" disease and other public health debacles. With the British government recommending that parents limit the amount of time children use mobiles, operators have decided to limit the amount of marketing aimed at younger customers. The threat of lawsuits from the US is likely to bring further caution.

In the past, technological innovation has always rescued the industry, particularly in the mid-1990s when the arrival of higher-quality digital handsets rejuvenated the flagging analogue market. But it remains unclear whether higher-speed Internet access promised by the latest models will have the same effect.

Handsets using this high-speed system, known as General Packet Radio Switching (GPRS), have been slow to arrive in bulk and may prove as big a flop as earlier Internet access provided through Wireless Application Protocol (WAP) phones. The delay in GPRS is particularly worrying with third-generation networks around the corner: many customers will delay replacing their handset, on the grounds that it will be largely obsolete by next year.

On the other hand, mobile advances are often slow to catch on. Text messaging, for example, took five years before it rapidly gained users. Nokia and the stronger of its rivals can afford to wait, especially with all the revenue to come from orders to build third-generation network infrastructure. But other wireless operators who depend on investors' faith in the industry's unrealised prospects for growth have something to worry about.