This state, host to the Southern Governors Association's annual meeting, is in the throes of a recession, hit hard by unemployment that has now reached 11.6 percent, a level unknown since the Depression.

In North Carolina, the jobless rate is 9.2 percent and, as Gov. James B. Hunt has been telling everyone here this week, it climbed one percentage point in the last two months alone.

The nation's economic woes have come home to the South, or at least to large portions of it.

Jobs in the textile industry--the top employer in both Carolinas--have fallen 11 percent since last summer.

Agriculture, another major source of employment in the region, is being strangled by high interest rates, governors here say.

"High interest rates have created an economic crisis of major proportions," said Democratic Gov. William Winter of Mississippi.

In Tennessee, the jobless rate, now 10.6 percent, is "unacceptably high," said Republican Gov. Lamar Alexander.

"The South's economy is more integrated into the national economy than it once was," said Jesse White, director of the Southern Growth Policies Board.

"The good news is: That has allowed us to increase our per capita income. The bad news is: We are now more subject to the same business cycles as the rest of the country."

Not all of the Sun Belt has been hit equally by the nation's economic woes. Oklahoma has the lowest unemployment in the nation (5.2 percent) and Texas, Florida and Virginia have unemployment rates below the national average.

But, said Virginia Gov. Charles S. Robb of his state's 7.1 percent jobless rate: "That is higher than we like or are used to."

In fact, some sections of Virginia, such as the textile and furniture-manufacturing Danville area, have 12.4 percent unemployment, a rate that mirrors the troubles of its southern neighbors.

The economy has been a main topic of the governors' working sessions and it is also topping their list of political concerns. Among the Republicans in particular, there is an thinly disguised anxiety about the effects of the Reagan administration's economic policy on the fall elections.

"If it works and we get people back to work and bring inflation down, we'll be in terrific shape. I sure hope it happens in the next couple of months," said Gov. Christopher Bond, a Republican from Missouri. Turning to an aide, Bond quipped: "Isn't that the party line?"

Southern Democrats are convinced that the region's economic woes will play to their advantage this fall, overriding whatever lingering loyalty there is to President Reagan and his programs.

"The popularity of the president is still certainly strong in this state," said Gov. Richard W. Riley, a Democrat from South Carolina. ". . . But in terms of November, I expect the popularity of the president will be less of a political factor than the state of the economy."

Reagan supporters in Mississippi are disappointed, said Gov. Winter. "They wanted him to get certain things done -- like reduce the federal deficit--the opposite has happened. Like lower interest rates--the opposite has happened. I think this is where they are beginning to part company."

The downturn in the local economies can be almost entirely traced to the national economic picture, state officials here said. Industries that are suffering the most are those tied to construction and to consumer goods, such as textiles.

In a speech to the governors, William Klobman, president of the American Textile Manufacturers Institute and chairman of Burlington Industries, reported that textile sales were down 6 percent compared with last year.

And for those looking for relief, there was more bad news from Felix Rohatyn, the banker who helped keep New York City solvent several years ago. He told the governors the outlook for the national ecomony was "at best unclear and probably grim."

Some of the southern states, coming out of a period of high growth, expect to be able to bounce back once the national recession has receded.

In South Carolina, for instance, state officials contend that economic indices show the state is poised for another boom.

While the South managed in the past decade to increase its average wage from 60 percent of the national average to 85 percent, there are signs that the region's fast growth has begun to slow down.

For instance, there has been little increase in the average wage southerners have earned since 1975, and per capita income in the South has barely increased compared with the rest of the nation.

Several governors have stressed that the key to the South's continued economic improvement lies in the region's ability to provide services and, in particular, education.

"If the South is going to be able to compete economically, it can do so only if it increases its level of education attainment," Winter said. "Until we equalize education opportunity for all people in all areas, even in the most remote rural areas, we won't achieve our goals."