ON THANKSGIVING morning in Plymouth, Mass., a small band of townsfolk in Puritan costumes will reenact the Pilgrim's procession of that first Thanksgiving 359 years ago. And, much in the manner of the original group, this year's marchers wil be looking over their shoulders wondering whether the Indians will appear and what they'll do.

Back in 1621, the Indians did show up in response to Gov. William Bradford's suggestion to Massasoit, chief of the Wampanoags, that he drop by and bring a few friends. Massasoit brought all 90 members of the tribe, who outnumbered their hosts almost 2 to 1 and so enjoyed themselves that they hung around for three days, feasting and frolicking.

This year, although not invited, the Indians will surely stop by again, but they will neither feast nor frolic. Led by the United American Indians of New England, including some descendants of Massasoit, they will be there to observe not Thanksgiving but a "Day of Mourning."

As Frank James, spokesman for the group, put it recently, "We'll be there to tell the truth and the truth is that the Pilgrims came to our shores, took our land and killed our ancestors." James, 56, a Wampanoag whose tribal name is Wamsutta, is quick to point out that the United American Indians are not radicals and their demonstration will, as always, be peaceful, even though he bitterly recalls, "the police greeted us with attack dogs a few years ago."

James is music director at Nauset Regional High School in Eastham, on lower Cape Cod, and plays many of the instruments he teaches. Commenting on the tradition of Thanksgiving, he said, "We have nothing to be thankful for."

And so, as they have every Thanksgiving Day since 1968, Indians from such tribes as the Sioux, Mohawk, MicMac, and Penobscot are expected to join the Wampanoags for their annual demonstration. They will shun the procession for a silent vigil in front of Massasoit's statue atop Cole's Hill overlooking Plymouth Rock and the harbor.

Later, they will form their own procession and head for Memorial Hall in the heart of town, where every Thanksgiving some 2,000 guests feast on a buffet-style Thanksgiving dinner. Once more the Indians will shun the feast and resume their vigil until sunset. Mourners at past demonstrations have numbered as few as 125 and as many as 500 Indians.

Reminded that last year a Plymouth clergyman's wife complained "the Indians never let us know what they'll do," Frank James chuckled. "We like to keep them guessing." But Richard Nagle, Plymouth's police chief said, "We don't expect any trouble."

Latest cause for anguish among Indians in the Plymouth area was the 1979 refusal of the U.S. Supreme Court to overturn a lower court ruling that the Wampanoags have no just claim to 11,000 acres in the town of Mashpee, some 20 miles south of Plymouth.

Indians however, are not the real source of uneasiness in "America's Home Town," as Plymouth styles itself. There is Pilgrim Station, a nuclear generating plant that transmits its 670 megawatts 40 miles north to Boston Edison Company, its principal owner.

Although Plymouth Station has had its problems (including an expensive alteration after Three Mile Island), it has largely escaped the fierce opposition that has bedeviled other nuclear plants, notably unfinished Seabrook in neighboring New Hampshire. Indeed, survey after survey among Plymouth residents have given the plant and Boston Edison votes of confidence by comfortable margins.

As Mark Johnston, former director of the Old Colony Memorial, a weekly newspaper in Plymouth, put it, "It's hard to get mad at somebody who throws all that money at you."

All that money is the $55 million in taxes Boston Edison has paid to the town since 1868, when they broke ground. Today one out of every three dollars in Plymouth taxes comes from Boston Edison.

One resident, expressing his anti-nuclear viewpoint, grumbled, "What good is the money if your kids turn purple and shrivel up?" Most people, however, accept the nuclear giant in their midst with the same indifference with which they greet the 1 million tourists each year.

To nobody's surprise, the 1980 U.S. Census revealed that Plymouth has a population of 32,500 -- up a mind-boggling 92.2 percent over the 1970 figure. Some 17,000 newcomers, drawn as to a lodestone by a shrunken and stabilized property tax rate ($22 per thousand), brought with them the problems of growth. New homes meant more schools. Four new ones were added. More people demanded more services -- on duty went 75 more policemen, 112 more firemen, according to town assessor George Moody Jr.

Even so, Plymouth has accomodated itself to the growth without missing a beat -- or a chance to sell souvenirs. Its claim to the title "America's Home Town" is more solid than ever: It now has both a McDonald's and a Burger King, plus a fair quota of pizza parlors.

And it boasts the only winery in the state, on the site of the Plymouth Cordage plant, once the world's largest rope-maker, where in 1916 the star-crossed Bartolomeo Vanzetti helped foment a bitter strike, the wounds of which never wholly healed. Eventually, the cordage works fell victim not to Vanzetti but to the Great Depression. Then the automobile opened up America's Home Town to thousands who had read about it and came to see for themselves.

So today, despite growing pains, Plymouth has much to be thankful for. The cranberry harvest, to be sure, has fallen to barely a million barrels -- down 15 percent for want of rain -- but at $29 a 100-pound barrel, growers will pocket record prices.

Businessmen are grateful that, ignoring high-priced gasoline, the tourists still come -- and not just in summer. With a full week of festivities starting Sunday, Nov. 23, Plymouth expects to entertain the usual 25,000 Thanksgiving visitors, some from as far away as the West Coast.

There will be plenty of things for them to do besides watch the feasting "newcomers" and the fasting native Americans. The highlight of the week, of course, is that procession up Leyden Street (the oldest one in a town full of old streets) to the First Parish church for the traditional Thanksgiving services.

Most museums will be open -- and the town fairly bursts with them, including a wax one. Plymouth Plantation with its thatched roofs and open-hearth cooking will take you back to the 17th century. On the waterfront you can enter The Cranberry World, one of the newer exhibits. And, next to The Rock itself, the most popular exhibit sits at dockside waiting to be boarded. It's the Mayflower II, proud flagship of the town.

Thus, despite the erosion of change, much of the Plymouth tradition remains, and for many townspeople there is the comforting thought that, in Ernest Downson's words, "When the feast is finished and the lamps expire," America's Home Town will be their own again.

One tradition immune to change is the Yankee penchant for salty humor. They tell the story here of a tourist making small talk with a policeman shepherding the crowd into Memorial Hall for that famous buffet-style Thanksgiving dinner. "A lot of weird-looking characters around here, aren't there, Officer,? the tourist joked.

The policeman looked him up and down slowly, nodded, then replied, "Sure are -- but they'll all be gone by the weekend."