Evidence is growing of a major push by European companies, particularly British, German and Swiss, to invest in the United States - a movement that looks like it will intensify in 1978.

European firms with money to invest want to increase their access to the world's biggest, market. This desire coincides with a weak dollar, the availability of small - and medium-sized American companies because of the depressed state of Wall Street, and European belief in the longer-term stability of the American economy. There is still a strong emotional attachment in the European business community to the view of the U.S. as the "last bastion of free enterprise."

In the past two months alone, the board of National bid from the British-Dutch multinational corporation Unilever, Bayer AG of West Germany has offered $275 million for Miles Laboratories, and Nestle of Switzerland has put in a $277 million offer for another U.S. pharmaceutical company, Alcon Laboratories.

British acquisition for the year passed the $1 billion mark by mid-December (including Unilever) - equal to the total for the previous three years, and the German appetite for American acquisitions reportedly is running high.

"There is tremendous additional interest in investmen t in the U.S. It comes in all shapes and sizes, especially from Germany," said Bart A. Smit, an Illinois trade representative.

Denis E. Rufin of the Virginia Trade and Development Office in Brussels gives a telling example. At a seminar for 85 Swiss businessmen held in Berne in early December, representatives of 28 U.S. states showed what they had to offer.

"Twenty -seven of the Swiss businessmen told me they wanted to build a plant at some point in the United States," said Rufin.

James Steward, of Chase Manhattan in London, believes the moves are part of a long trend, noting that since 1972 the flow of capital across the Atlantic has reversed itself.

"For years European companies were the target of American investors. Suddenly the flow of capital has been reversed, and there is an increasing propensity by Europeans to want to get a slice of the U.S. action," he said.

Steward believes that the underlying economic factors involved are so strong that the present trend will continue and even accelerate in 1978.

Financial publications have added up the individual boardroom decisions to pronounce it a significant trend for the United States.

The cover of the Dec. 17 issue of Economist magazine featured a map of America with a "25 per cent off" tag attached.

And under the headline "America Going Cheap," the magazines's editorial read: "American industrial corporations are on offer this Christmas at clearance sale prices. Foreigners should rush to buy, expecially those whose central banks have accumulated more dollars than they know what to do with."

The Guardian's investment correspondent Robin Stoddart wrote recently that British companies are almost falling over themselves in their eagerness to invest in the United States.

He reported, "Every chemical company worth its salt, both here and on the continent, has indicated that a major foothold in the world's biggest market is regarded as an essential ingredient for success."

Chemical and pharmaceautical companies are indeed active, but recent moves have involved shoes, insurance, roller bearings, sugar alcohol from corn cobs, auto mufflers, banking and even a French company's 50 per cent acquistion in uranium mining rights in southern Utah.

Nathan Gelber, an associate director of Irion Bank in London, believes the change over the past two years is that medium-sized companies are joining the multinationals in wanting to extend into America.

"It has become fashionable for European companies to invest in the U.S. - and to some extent political instability in Europe is a factor," said Gelber.

The reasoning behind the Unilever decisions gives clues to some of the factors involved.

Unilever had money to invest, America accounted for less than 10 per cent of its total sales, its main growth had been coming from "risky" investments in the Third World and expansion in Europe was looking tough.

As are most of the European moves into the United States, the deal was a mutually agreeable acquisition of a well-established company with similar interests.

Unilever's managing director Sir David Orr said that to try break into a new market from scratch would be a "helluva risk."

In the past few months there also has been a remarkable rush of Swiss chemical companies into the United States. The moves have been triggered by the cheap dollar, lower U.S. production costs than in Switzerland, and the danger that Swiss exports to the United States would be priced out of the market.

Ciba-Geigy has devoted between 20 and 25 per cent of its group investments to North America in the past two years.

In early December, Britain's General Electric Co. hired award-winning businessman Geoffrey Cross, a British-born American citizen, to go to California to look for electrical and electronics companies to buy.

GEC quite simply wants to get some of the $51 billion American electrical market. And as Cross says, "It's quicker to buy into a U.S. company - that way you get a share of the market straightaway."

The industrial holding company Thomas Tilling has had its deputy managing director Collin Draper living in the United States since March. He is looking for companies to buy under a multimillion dollar U.S. investment program.

New York state, which has been one of the most successful in attracting European investment, is so confident the time is right that it has launched a $20,000 advertising campaign in European business newspapers and magazines - including full-page advertisements in the Financial Times, pushing the slogan "What New York offers your business, the rest of American can't."

Merchant Banker's Morgan Grenfell, in a survey of direct investment into the United States, published in early 1977, commented: "The majority of all acquisitions in the U.S. by foreign companies in the last decade appear to have been successful in financial terms, and in some cases spectacularly so."

In other forms of investment, stock portfolios and real estate, the picture is not so clear. Wall Street is seen here as a bad performer over the past two decades and, as a trading market, not so suitable for medium-and long-term investment.

But now stockbrokers are saying the Dow Jones is so low American stocks must be a bargain - mustn't they?

Mark Vaughan-Lee, a director of Drayton Montagu Portfolio Management said, "Investors thought things would pick up in early 1978. Now they don't know when it's going to happen. But in the longer term they believe in the American capitalist system and in the American ability to make its administrative system work.

"There was interest in the later months of 1977 but this has now fallen off. There is lack of confidence in Wall Street," he said.

But interest is growing from mutual fund managers (until trusts in the Britain). One of the better performers in Britain last year, Framlington Unit Management, is setting up a new trust in January based on North American stocks. One of the stockbrokers who will be handling it, Christopher Anderson, said, "We do feel if there is a general world recovery it will be American-led."

American real estate, according to one investment banker, has more of a smell of tax haven than investmentabout it. But British pensions funds over the past three years have dipped their toes in the water. Nine or ten British pension funds including British Rail are grouped together in a property trust that has $12 million invested in property largely in the Southeast.

Southeby's, the auctioneers who set up an American operation a year ago, say there are the first signs of a European interest in American farmland, which is now cheap compared with German or Dutch land.

Two estates were recently bought by Germans, and Stanley Clark of Southeby's says he expects suchinvestments to increase in 1978 if the dollar stays low.