Visitors to the United States who need to resort to money machines to bolster their holiday funds may find themselves having to queue behind people who are beavering away at the screen with rather more concentration than usual. There may even be the occasional cheer, or shout of dismay.

These mesmerised Americans are not wrestling with the universal headaches of automated banking - trying to retrieve a swallowed card or to remember a forgotten PIN. Their behaviour is the result of a more complex activity - the electronic world's latest contribution to computerised personal finance.

Instead of squandering money, these people have come to their 'hole in the wall' in search of profit: they are buying and selling shares.

Citibank, a subsidiary of Citicorp, America's largest bank, claims to be the first financial institution to provide its brokerage customers with the means to deal in stocks, mutual funds and other securities through automated teller machines (ATMs). Newly adapted machines were unveiled this month in Chicago, Miami and New York; the technology will soon be installed in the bank's 1,800 machines around the United States.

The do-it-yourself system is simple and has the advantage of freeing those with enough financial nous to handle their own affairs from being pestered by pushy brokers. After slipping their ATM cards into the machine, users can examine a breakdown of their portfolios that shows the number of shares they have, the current price per share, an up-to-date total market value of their position, and the latest available price on any common or preferred stock of their choice.

Should they wish to invest, say, in Microsoft, they simply touch the 'Buy Stock' option, enter the stock symbol, and punch in the number of shares they want. They can instruct the ATM either to purchase shares at the latest market price, or set a figure at which they want their purchase to be activated. The funds come from whichever of their Citibank accounts they wish to use.

The service is around the clock, 365 days a year, and instantaneous, although orders placed after-hours must wait until the next market opening before they are acted on. Selling is done much the same way. Proceeds from any sale are automatically deposited into the user's checking account, minus the minimum dollars 38 ( pounds 24) commission Citibank charges - somewhat higher than the cheapest available discount brokerage prices.

Such dealing on ATMs is the latest addition to a growing list of technologies that make it easier for America's 52 million individual investors in stock to run their own portfolios.

Several million people in the US and Europe already buy and sell shares (and other investments) by using PCs to access on- line brokerage services. These days, such transactions can be done during a domestic airline flight, using the on-board, modem-equipped telephones.

One of America's largest discount stockbrokers, Charles Schwab & Co Inc, has for some time been marketing software that connects its clients with the company's central computer, allowing them to manage their money by trading stocks, corporate bonds, options and mutual funds in the privacy of their home or office.

The trend seems set to continue: industry analysts say that by the end of 1994 more than half of the US workforce will have access to a PC; already 31.8 million American households, about one in three, have computers. The public is becoming more financially literate in the workings of the markets.

'It's all about control,' said Tom Taggart, a Schwab spokesman. 'Individual investors are thought of by Wall Street as stupid, but that's not true. In fact, they tend to be smart because they are controlling their own situation. No one can say a broker with 50 clients is going to look out for you as much as you will look out for yourself.'

But aren't those ATM queues long enough already, without getting stuck behind Gordon Gekko, when all you want is to withdraw dollars 10 to cover your lunchtime sandwiches? And what happens when the market crashes? Won't every airport foyer become the backdrop for a riot?

Citibank says its research shows queues are unlikely to be affected by its scheme, largely because so many cash machines are now available. A Citibank spokeswoman said: 'We have found that in tests there was no real problem.'

Mr Taggart, who offers a rival service, is not so sure: 'I wouldn't want people looking over my shoulder while I bought and sold stock. Nor do we think our customers would like to stand out in the cold to do their business, especially in areas where it's not safe.'

Whether Americans take part in any significant numbers remains to be seen - Citibank won't say how many users its ATM stock-dealing service has so far attracted. But the world's stockbrokers seem set to be a dying species. Next time you go to an ATM in America, don't buy into bowler hats.