JEREMY TUNSTALL is a professor of sociology at the City University in London, with several academic studies of journalism and advertising to his credit. That, and the title of his new book, with its unfortunate understones of anti-American paranoia, might lead American readers to fear the worst.

They would be wrong, though. In spite of its title, this book is anything but a routine denunciation of American "media imperialism." It is serious, learned and fair-minded study of the complex causes and complex implications of the dominant role of American media, or rather, as his subtitle emphasizes, "Anglo-American media," in the world.

Tunstall is notably cool in his dissection of what he calls "the often ferocious and often self-contradictory arguments" put forward on the subject of alleged American "media imperialism," by Herbert Schiller in a 1969 book, Mass Communications and American Empire, and since then by others writers - most of them, interestingly. American radicals rather than foreign nationalists. These crude versions of the media imperialism thesis, Tunstall contends, are both exaggerated and at the same time too restricted.

They are exaggereated because they are too narrowly based on the evidence of a boom in overseas sales of cheap, often schlocky, American television entertainment in the 1960s - a boom which has considerably slackened since then, and indeed has even been partially reversed as the United States imports products from Britain and other countries.

The high point of America's media influence generally, Tunstall points out, like the high point of its political, ideological and cultural influence, came in the decade from 1943 to 1953. That was the time when, as Leslie Fiedler wrote, "A specter haunts Europe, the specter of Gary Cooper." (The zenith of U.S. influence in Latin America was also reached in the 1940s.)

Germany, Japan and Italy all had their postwar media fare more consciously and effectively shaped on Anglo-American lines than the postcolonial countries in the 1950s and 1960s. And before Europe and recovered from World War II the sheer magic of American prosperity - then, but not now, unparalleled - gave an "almost hypnotic attraction" to Hollywood movies, the overseas edition of Life magazine and even to the American Forces Radio Network.

Conventional analyes of the influuence of the American media are at the same time too "weak" and superficial, Tunstall believes. They underestimate the number of different media in which U.S. influence has been dominant. And they also ignore the length of time over which that influence has been exerted.

Not only television, but also radio, film, advertising, the popular song and even the mass-circulation newspaper and the magazine were essentially American inventions, Tunstall argues - although at different times Britain, France and Germany all contributed some important ideas and techniques in different media.

Tunstall even floats (but, for this reader, does not adequately discuss) the tantalizing idea that all media, including the newspaper itself, are essentially American - rather than merely phenomena that developed faster and more prolifically in the United States - because of certain essential characteristics of 19th century history in the United States.

Certainly, he points out, American influence was crucial for the development of the British press as early as the first half of the 19th century, and the British popular press not only followed long after, but was directly modeled on, its precursors in the United States. In Germany, too, the press empires of the early 20th century, destroyed Hitler and Hugenberg - Ullstein, Mosse and Scheri - were influenced by American technology, American commercial ideas, and executives trained in America.

It was in New York specifically, around the year 1900, that the various existing media were for the first time shaped into a comprehensive media industry, involving magazines, advertising, popular music and films, and based on two older traditions, the mass-circulation newspaper and the live popular theater.

One of the most original parts of Tunstall's thesis is that, all along, the British media have played the role, not of a progressively defeated competitor, but of a prosperous junior partner to the dominant American media enterprises. He points out that, of the 20 or so great corporations which dominate world media exports, some five are British; that British media exports to the rest of the world are still approximately one-third, by cash value, of U.S. exports, that, for example, the most dominant single media enterprise in any one fields is the 75 per cent British-owned TV sales organization, Visnews, whose news in 1975 was - so the organization claimed - "seen on some 99 per cent of all the television receivers in the world," in 98 countries.

Curiously, Tunstall suggests, countries such as Britain (and, on a regional scale, Italy, India, Mexico or Egypt) which are major media exporters are also significant importers. This suggests the model, not of American media corporations forcing their products on unwilling markets by price-cutting, but rather of a world media system in which countries are receptive to American influence to the extent that their own societies approximate America in the state of their media development. Or - less attractively - it suggests the model of a world media cartel in which the junior partners also have their share.

There are many - indeed, perhaps, too many - other sharp peerceptions and suggestions in this book. Tunstan is enlightening, and sometimes dry, on the way in which the disciples of marketing research analyst Paul Lazarsfeld, often subsidized by U.S. media corporations, disseminated their theory of communications in the post war world with a shrewd sense of public relations. They were careful to talk about "the free flow of information," be points out, and not about "free trade for media products."

The most serious criticism that can be made of Tunstall's work, I believe, is that he has fallen between the two stools of history and theory. This is in many ways a pioneering history of the spread of American influence on the world's media. It is also the sketch for a most original and plausible theory of how and why that influence became so dominant. But too often the account of some important subordinate relationship - that between Hollywood and the Italian film industry, for example - is left tantalizingly brief. And too often the precise way in which Tunstall himself thinks a relationship worked is left unresolved between two or three alternative hypotheses too tolerantly discussed.

Still, Professor Tunstall is young, energetic and talented. He has time to write both a more extended history of an important topic, and a more precise and more personal theory to explain it. Both will be worth reading if he does.