It was 1963, Eloise Stevens recalls, and she was returning from a vacation in Clearwater to her home in Warren, Ohio, when she spotted a highway sign promoting one of the new developments along Florida's Gulf Coast.

It offered a house and a lot and year-round warm weather, all for less than $6,000. A few days later, back in Ohio, she made a decision.

"I said, 'You know, I think I'll buy one of those houses,' " Stevens said.

A few years later, Stevens, the personnel director for the post office in Warren, retired in Pasco County, just north of St. Petersburg and Clearwater. She was something of a pioneer. Back then, Pasco County was far from being a retirement haven.

The 1970s changed all that. Tens of thousands of people, many of them retired from government service or blue-collar jobs, followed her to Pasco County. Today Stevens is the Democratic chairman in the fastest growing county in the fastest growing congressional district in the United States.

This is the 5th District of Florida, which stretches more than 100 miles between the retirement communities here along the Gulf Coast and the clusters of garden apartments for young single people north of Orlando in Seminole County.

Between 1970 and 1980, according to census figures, the 5th District grew by 94 percent. Its official 1980 Census Bureau population of 880,078 makes it the largest congressional district in the country. Bill McCollum, the first-term Republican from this district, represents more than twice as many people as does Democrat Mary Rose Oakar of the 20th District of Ohio on the West Side of Cleveland.

If Ohio is a place that Americans are moving from, Florida is one of the places they are moving to. During the 1970s, Pasco County's population grew by 155 percent, from 75,955 to 194,123. During the same period, Seminole County grew by 114 percent, from a population of 83,692 to 179,752.

The shift of population from the Northeast and Midwest to the South and Southwest that these growth figures exemplify will soon be followed by a shift in political power-- Ohio, for example, will lose two seats in Congress as a result of redistricting following the 1980 census, while Florida will gain four seats.

In large measure, the future of politics in the country belongs to places like this, which can expect continued growth in population and political power. And it is the Republicans who look most confidently to that future. The Democrats' traditional base in the Northeast and industrial Midwest is shrinking while the Sun Belt grows more Republican each year.

But up in Tallahassee and in state capitals across the South and into the West, the Democrats are not conceding the future of the Sun Belt to their GOP opponents. Florida Democrats believe that two of the state's four new congressional seats will be theirs and that they have at least an even chance of winning a third.

If they are right, the future for the Democrats in the Sun Belt may not be as bleak as it first appeared. Population growth in Florida during the 1970s was not all that different from other southern and western states-- it included not only retirees who have traditionally settled in Florida, but also tens of thousands of young people attracted to Florida not just by the weather but by a healthy economy.

The presence of all these newcomers has made Florida and other southern states less Democratic over the years, but it does not necessarily mean that they will continue on the road to Republicanism.

The very growth that has made the 5th District and others like it bulge at the seams makes the future of politics in these places uncertain. The people who moved to the 5th District in the last 10 years, said Gary Smith, chief of staff to Florida's Democratic Gov. Bob Graham, are in large part without any loyalties to individual political figures or institutions in their new home state.

"The people don't have roots or traditions," he said. "It is a very volatile situation."

The 5th District stands as a monument to the proposition that even the most careful gerrymandering cannot guarantee election results.

After the 1970 census, the Democratic-controlled Florida legislature sat down to redraw congressional district lines. Being fair to the Republicans was not one of their priorities, and so they created the 5th District. It dips into Clearwater, taking in a large portion of that city's black precincts. To the east, it slices off a Democratic section of Orlando.

The shape of the district fit perfectly with the political aspirations of one of the people who helped draw it, State Sen. Bill Gunter, who had been a member of the legislature's redistricting committee. And in 1972, Gunter ran for Congress in the newly created district, easily winning with 56 percent of the vote even as Richard Nixon was swamping George McGovern in Florida and elsewhere in the country.

But then a funny thing happened to the Democrats' careful plans for the district. Gunter's ambition led him next to an unsuccessful run for the Senate in 1974. To replace Gunter in the House that year, the voters of the 5th elected a Republican, and they have elected Republicans ever since.

The first was Richard Kelly, a flamboyant politician who later was convicted in the Abscam investigation. He was followed by McCollum, a young, diligent lawyer from Orlando with a much different personality.

Despite their differences, these two Republicans had one thing in common -- they were both elected by Democrats.

In 1970, for example, Pasco County had 21,522 registered Democrats compared with 12,160 registered Republicans. Ten years later, the Democrats still enjoyed a healthy edge in registered voters, 63,930 to 42,567.

These new voters came from Illinois, Michigan, Ohio and New York. When they hold the annual Warren, Ohio, picnic in Clearwater, some 300 people, including Eloise Stevens, attend. There is a New York club in Pasco County, a Pennsylvania club, at least five Italian-American clubs.

The modestly priced housing attracted a different kind of retiree than those who settled in such posh enclaves as Naples, farther south along the Gulf Coast. The new residents of Pasco County tended to be former blue-collar workers, union members, many of them lifelong Democrats.

Their influx, according to Democrat Ted Williams, the longtime elected property assessor, transformed the politics of the county. No longer was Pasco County a sleepy rural area dominated by citrus, cattle and a well-entrenched Democratic organization.

Power followed the people, in Pasco County as well as the country at large. Where once three of the five county commissioners were elected from the rural, eastern end of the county around Dade City, now three of the five come from local districts on the west coast among the retirement communities. Where once the Democrats easily dominated local politics, as they did throughout the rural South, the Republicans are now a serious force to be dealt with.

In 1972, a good year for the GOP everywhere, the Republicans gained control of four of the five county commission seats. By four years later, the Democrats had made a dramatic comeback and held all five seats. But the 1980 election cut the Democratic edge to 3 to 2. The struggle for control of the local government is likely to be as uncertain and turbulent in the 1980s as it was in the 1970s.

At the other end of the 5th District, in Seminole County, the growth was almost as dramatic. But it was a different kind of growth. It was not retirees who moved to Seminole, but young people attracted by the booming economy around Orlando.

This difference showed in the voter registration statistics. In Pasco County, the number of registered voters kept pace with the overall growth, more than tripling during the 1970s. But younger people are less interested in government and politics than their elders, with the result that in Seminole County the number of registered voters actually declined in 1974 and again in 1978, both nonpresidential election years.

The nonvoting young people of Seminole County are one of factors that make the future of politics in this area uncertain. So are the political attitudes and activism of the younger people who, in increasing numbers, are moving to Pasco County to provide services for the retirees.

And so finally are the opportunities and problems that the flow of people and power to the Sun Belt is bound to produce in the years ahead.

Roger D. Neiswender is the county administrator of Seminole County, a nonpartisan job he has held for six years. From that vantage point, Neiswender has watched the explosive growth that the 1970s brought, witnessed the decline of the once-dominant county Democratic Party in a bitter split over the issue of continued growth, and thought a great deal about what this will mean for the county in the 1980s.

He could have been speaking about much of the Sun Belt when he said:

"There are some conflicts coming. Those people who left the industrial centers of the North are coming here fleeing high taxes and old, decaying facilities in the cities. They are anti-tax but high-service oriented. Now, when they complain about the level of services here, we ask if they recall how much they paid in taxes where they came from.

"Sooner or later, this is all going to come out in the political process. It will take time, though. It will take time for the public to understand that the cost of all this growth has not been paid for. But somebody, one of the parties, has an opportunity here."