Everywhere in St. George's - on the beach, in the restaurants, on the main seaside drive - relaxed, animated groups of people are tentatively proclaiming a return to normality.
Even the well-armed foreign soldiers are visibly less tense than they were a week ago. They mingle freely with local residents in this small tropical port.
United States Army officers and thoughtful Grenadians, however, worry that small groups of ex-Grenadian Army (PRA) members could be hiding in the hills, perhaps regrouping for terrorist attacks.
United States paratroopers bathing at the beach and US mission members dining on the crowded terrace of the Red Crab restaurant look distinctly vulnerable to such attacks. And even many of the Grenadians and Americans who want to see US troops quickly withdrawn recognize that Grenada will continue to have some real security problems for the next few months.
The challenge, these sources say, is to handle the security problems with as little US military involvement as possible - and in a way that least infringes on the reestablishment of Grenadian sovereignty and normal political functioning.
US military sources estimate that it will take several weeks for whatever PRA elements remain in the hills to reorganize.
Any such PRA groups will face difficulties in obtaining supplies of arms. But many informed observers here say that the radical forces probably have access to arms caches hidden in the mountainous interior by the previous government. Some prominent Grenadians also fear that if US naval surveillance ends, resistance forces could also be resupplied by sea.
Meanwhile, the US Army is using all the high-technology methods at its disposal, including sophisticated radar, to ferret out any guerrilla elements before they can start any attacks.
The disquiet that many Grenadians feel about PRA members still hiding out has its roots in the shock of the Fort Rupert massacre, when Prime Minister Maurice Bishop and about 200 demonstrators were gunned down.
Until ''bloody Wednesday,'' as the Oct. 19 massacre is called, the killing of political opponents was unknown on this small island. Many Grenadians have still not shaken off the unease brought on by that day's events.
But even some well-known islanders asked that their names not be published because of their fear of possible reprisals.
As a prominent Grenadian said, ''If the soldiers at Fort Rupert could gun down their own friends and brothers from the New Jewel Movement (Bishop's political party), they are obviously madmen capable of anything. Would they stop at killing anyone they think is collaborating with the American invaders?''
Grenadians' fears are currently being kept at bay by the presence of 2,300 American troops on the island, in addition to an ever-changing number of support personnel such as military engineers. US Army sources speculate that some of these forces will remain until at least Dec. 20, when, under the war powers act, President Reagan's ability to send in troops for 60 days without consulting Congress expires. The probability of US troops remaining in Grenada for a few more weeks was heightened when guerrilla snipers fired at US troops recently.
The soldiers continue to stop people coming into the country and at roadblocks, checking their names against a computer list of alleged former members of the PRA.
In some instances people have been detained because they have been denounced by Grenadians bearing grudges against them. There have also been some cases of mistaken identity.
An example of the latter occurred last weekend when Samuel Braithwaite - the son of Nicholas Braithwaite, acting head of Grenada's governing advisory council - was detained with his hands tied behind his back for an hour as he was coming in from Guyana. Thirty people have been deported in recent weeks - at least two of them Americans - and 1,100 Grenadians and Cubans have been detained since the US intervention.
Most observers feel that some sort of peacekeeping arrangement will be necessary when the US troops leave, since Grenada no longer has an army. It will also take time to train a police force capable of handling any major security problems.
Many Grenadians feel that elections cannot be held in less than one year's time. They estimate 1,000 to 1,500 troops will be necessary to keep the peace until elections.
Some prominent Grenadians and US Army sources mention these potential security arrangements:
1. Large-scale US presence in Grenada past Dec. 20.
Such an option is possible, by considered unlikely because of political opposition in the US. A continued US presence could also reduce Grenadian support for the US. An influential Grenadian says, ''The US is very popular now. But if you stay too long, you will be blamed for the various security and political problems arising along with way, and your support will start to erode.''
A moderate Grenadian adds, ''If US troops are here for long, it might create doubts in many people's minds about the fairness and freedom of the elections.''
He and others are concerned that Grenadians might begin to suspect that the electoral process, including the preparation of voter-registration lists, was in some way influenced by the presence of US troops.
Some say that a continuing US presence would keep Grenada a subject of prolonged international controversy. They state that they prefer an arrangement that would keep the island out of the East-West tug of war.
2. A ''policing force'' of Caribbean and US troops.
Under such an option, described by US Army sources, US participation would be kept to one battalion. Grenadian sources say that this arrangement may still present the problems outlined in the first alternative.
3. A Commonwealth force.
This alternative is favored by many Grenadians who feel that it would be in keeping with Grenada's status as a member of the Commonwealth. Although Britain might refuse to participate in any such force because of its original objections to the US intervention, a force could be made up of Canadians, Nigerians, Australians, and others, say some Grenadians.
4. A United Nations peacekeeping force.
This option arouses less enthusiasm than the Commonwealth alternative. Grenadians say there might be a language barrier between these UN forces and English-speaking Grenadians. They also say Grenada does not fit the classic UN peacekeeping situation - one in which the UN forces keep the peace between two disputing parties. Grenada, they say, needs a security force to root out whatever guerrilla or terrorist forces remain.
The US could have a role in a UN force, much like US peacekeeping troops in the Sinai.
5. A peace force of Caribbean nations.
Members of the Organization of Eastern Caribbean States could compose a peace force, and Commonwealth troops could act as a backup rapid deployment force in case of a sudden deterioration of the security situation.