High on a hill overlooking this country's storybook harbor, where cruise ships from a half dozen nations bob lazily in the sun and children run from gingerbread houses to greet the arriving tourists and hopefully sell them something, sits the home of Grenadian Prime Minister Maurice Bishop.

Visitors are seated on the wide and breezy veranda and left with the magnificant view and the soft disco strains of Radio Free Grenada to entertain them while they wait for "Maurice," or the "P.M." as he is alternately known here, to appear.

Tall and lanky, he strides in with 36-year-old assurance, collapses in a chair and asks to borrow a cigarette. He taps his foot, strokes his beard and waits impatiently for the questions.

"We have nothing against the people of America," he says in answer to a request to clarify Grenadian relations with the United States over the 18 months since his government took over here in the English-speaking Caribbean's first coup d'etat.

"Our quarrel with America is against the system of imperialism, pushed by the [Carter] administration, the State Department, the National Security Council, the business lobby, the media and individuals."

Eventually, Bishops says, Americans are going to understand that their government is considered "rapacious, violent, terrorist and antidevelopment by most people in the world."

Switch scenes for a moment, to a brightly lit U.S. government office, where the air conditioning hums in the background and muffles the heavy traffic outside.

"We have problems with human rights," in Grenada, the State Department official says, "with the suspension of the constitution, no elections, harassment of the opposition. But what really gets our goat is the anti-U.S. rhetic. We get blamed for everything."

There is a feeling, when talking about Grenada either with its own officials or those of the United States, that in addition to very definite policy disagreements, a basic personality clash exists between the two governments.

Grenada's new leaders, members of a plitical party called the New Jewel Movement, are young, brash and impatient. Finding few resources to deal with the domestic economic problems that are their primary long-term challenge, and still appearing unsure of how they want to reorganize the island's political structures, they have used strident criticism of the United States -- along with close friendship with Cuba -- as the focus of their government so far.

While little has changed in the way most people live their lives here, the new Grenada seen at international conferences such as last year's non-aligned summitt in Havana and the October opening of the United Nations General Assembly is outspokenly leftist.

"Why do people say things like that about us?" Bishop asks. "Because we have developed close ties with Cuba, and the Afgan vote" in which Grenada was one of only 18 countries that supported the Soviet invasion of Afghanistan in a U.N. ballot last January.

Grenada's foreign policy is one that, at the very least, has brought the island international attention after the long years when most people and nations in this country existed. It has also put a burden on the United States to live up to its professed policy of respecting "ideological pluralism" in the Caribbean and to learn how to deal with a "difficult" government in a minuscule nation whose 110,000 people and 133 square-mile territory can hardly justify what one Carter administration official says is close attention paid to its every move, "right up to the level of secretary of state."

The chronology of a year and a half of relations between Grenada and the United States is instructive both in its difficulty and what appears from both sides to be its futility.

Within a week after the coup, against a minor-league despot named Eric Gairy who had held power here for years through a combination of repression and popular lethargy, the United States had given cautious public approval to the new government. It knew little about Grenada's new leaders, just as it knew little about the island itself, except that some of them had traveled to Cuba in recent years.

Within a month, however, relations had gone from neutral to negative as then-U.S. ambassador Frank Ortiz traveled to St. George's with instructions to warn Bishop about developing close relations with Cuba. The new government -- almost as if it had been waiting for such justification -- publicly welcomed a Cuban naval vessel into port and a group of Cuban advisers.

While Bishop called for international aid to help the nearly bankrupt country, Ortiz was limited by U.S. congressional prohibitions to offering only grants of $5,000 each for specific development projects. For the new government, such amounts were insulting from such a wealthy neighbor. The United States had tried to interfere in Grenada's right to develop relations with whomever it wished, Bishop charged, and was prepared to withhold needed economic aid to pressure the island.

At the same time, the United States was stuck with the pressure of Gairy.

Unseated while visiting New York, he had taken up residence in San Diego and begun a series of radio broadcasts calling for a countercoup. The United States found it difficult to take Gairy seriously. Grenada took him very seriously indeed, or at least professed to, and the new government had yet another gripe against Washington.

Then came the problem of the ambassadors. Grenada was obviously unhappy with Ortiz, who had gotten off to a bad start with the new government. Washington was unhappy with him for other reasons and soon transferred him ot Guatemala. Sally Sheldon, a woman of more liberal tendencies, was sent in his place and things seemed to improve. But trouble started on the other end.

Kendrick Radix, who served both as Grenada's attorney general and ambassador to the United States and the United Nations, was recalled for pressing duties at home. In his place, the Grenadian government named Dessima Williams, a then 26-year-old former Georgetown University student who served as the island's ambassador to the Organization of American States.

For months now, the State Department has refused to formally accept Williams' appointment, without officially giving the Grenadian government a reason. State Department sources say it is because Williams was allegedly implicated in a gun-running scheme out of Washington in which two Grenadians were arrested immediately before the coup. Williams, they maintain, was spared indictment only because her OAS appointment gave her diplomatic immunity.

The United States also privately maintains that Williams implied to the State Department that a 56-year-old American woman arrested in the summer of 1979 on vague charges of counterrevolution would be released if the Justice Department would release the two Grenadians charged with violating U.S. arms control laws.

"This came right after the hostages were seized in Iran," one administration source said in Washington, "and people around here really hit the ceiling."

Grenada heatedly denies that any such implication was ever made and notes that the American woman was released even before the two Grenadians eventually jumped bail and returned to the island, where they are now considered national heroes.

Most recently, Grenada had charged CIA complicity in a series of bombings and protests against the government here. The administration denies it is trying in any way to destabilize the government and demands to be shown proof.

Bishop counters that "I don't know of any case where the CIA has left its calling card" since the intelligence organization's modus operandi is covert action. He charges that among other things the U.S. government has instructed U.S. tourist agencies to discourage customers from going to Grenada.

"That's ridiculous," says a U.S. diplomat in the regional embassy.

Still, Bishop says he would like to have good relations with the United States. "As far as I'm concerned, I've never made anti-American, anti-imperialist speeches for their own sake. There is nothing I would like better than to stand up and say that the U.S. testablishment is no longer waging an aggressive, imperialistic policy.

"It's like the situation with Gairy," Bishop says. "The United States has to stop this policy of picking up every latrine dictator. They say it's a 'severe embarrassment' that he's on the radio every day saying he's coming back. You don't want him, he wants to come back we want him back. "What's the problem?"

The United States says Grenada has never made a formal extradition request for Gairy. Grenada says it has submitted all the papers, and the Justice Department has stonewalled.

"The reality is it's just a lot of sand dancin' and 'bramblin', Bishop says. "That's a Grenadian phrase. I guess in black American, it would be the same as 'a lot of jivin.'"