A string of cars, station wagons and camper homes moves slowly between the corn and milo fields, rolling along the asphalt capillaries that lead from the main arterials to tiny towns like this.

The Republican call it "Caravan 1978" and from the lead car on back, it says so much of the Republicans' past fortunes and present misfortunes in Nebraska.

The past is in the lead: Anne Batchelder, state party chairman, wheels a silver Mercedes with a telephone - a fitting symbol of the days of Republican political prosperity here of days when the party filled the state's congressional delegation.Days when the GOP nomination assured election.

Toward the rear is the present: an old weathered maroon Chrysler with a missing hubcap carries the party's hapless candidate for U.S. Senate this yyear, Don Shasteen. He readily admits he is trailing Democrat J. James Exon, the state's popular governor. One poll, by the Lincoln Journal and Star, found Exon leading Shasteen by 6 1/2 to 19 percent.

Exon's commanding lead appears to assure that Nebraska, for the first time in the state's history, will have two Democratic U.S. senators - a stunning turn of events since registered Republican; still outnumbered Democrats in a state that historically has been perhaps the most Republican.

A Democratic evolution in recent years has brought two-party politics here, at the expense of the Republicans. So it is that their hopes for the future ride in one other car of "Caravan 1978," a car as nondescript as its black-suited, white-shirted, gray-haired occupant, Rep. Charles Thone, who has given up a safe House seat to run for governor.

Thone - or Charlie as he's known around here - leads in what is expected to be a close election. He has become, as a result, the great GOP hope for preventing a possible political wipeout of Republicans but his sure Republican congressional seat is up for grabs in a race that is a virtual tossup with large numbers of undecided voters, according to newspaper polls.

"Voters are getting more sophisticated," said Exon, who is getting more than half of the Republican vote, according to the polls. "They are voting for the man and not for the party."

Exon would succeed retiring conservative Sen. Carl Curtis, 73, who was first elected to the Senate in 1954 and who barely survived a 1972 challenge by a fringe candidate. Curtis, an ardent supporter of Richard Nixon, generally has been a rather backluster, ineffective senator.

The Democratic growth here has bot been without help from Republicans. Observers cite the Republicans' failure to develop new talent, the inability to accept new ideas, overall complacency and a divisive primary in 1970. Anne Batchelder's husband challenged the incumbent Republican governor that year, apparently helping lead to Exon's first election in 1970.

Then came 1976, Edward Zorinsky, a nominal Republican and mayor of Omaha, declared himself a Democrat after party leaders decided against him as a successor to then-Sen. Roman Hruska. Zorinzky won - the first Democrat elected to the Senate since 1934 - as did Democratic congressional candidate John Cavanaugh, and in one day of voting the Republican lock on the state's congressional delegation was broken.

Exon (pronounced Ex-un) describes himself as a moderate conservative who would be with President Carter on some issues and against him on "many things" - labor reform, full employment legislation, national health insurance. He did, however, support the president's veto of the public works bill.

His fiscal conservatism, he says, is based on a belief that "you can't keep spending more than you take in," but he sees the Democratic Party as the best vehicle for reducing inflation without destroying the social programs to which the party has given birth.

Such fiscal conservatism, or fiscal realism as the governor likes to call it, gives Shasteen little maneuvering room in a Senate race that has been without issues.

He has accused Exon of improperities in business solititation letters sent to the federal agriculture offices in Nebraska by the company in which Exon is the major stockholder. The effect of the allegations, generally regarded as somewhat fuzzy, has been to raise Exon's standing in the polls.

Shasteen told a breakfast gathering in neighboring Plattsmouth the other day: "We can, we must, we shall overcome the problems of extreme inflation, extreme deficit spending, extreme government regulation of our lives."

It had a good ring, but it was set aside at lunch in Gretna. There, he told elderly people at a federally funded hot lunch (suggested donation 50c) he would keep "your interests uppermost" in future legislation affecting Social Security.

Such is the Republican dilemma of campaigning against federal spending and then having to go in search of votes among those benefit from such spending.

So attention focuses on the governor's race and whether Republicans can retain control of that office and use it to rebuild their party to what it once was.

Thone is opposed by Lt. Gerald Whelan, - or Jerry as he's known around here - in what also is generally a race without issues. Reflecting that, Whelan stumped a suburban Omaha Rotary lunch last week on "The Importance of Irrigation," and added: "It's Charlie versus me. We're are different people, and it's people who run government, not issues."

To be sure, the Democratic surge in Nebraska was made possible because by the state party's generally conservative nature. "We're cracking the Republican's base of top management." Whelan said on a morning when labor and management representatives introduced him to telephone company employes arriving for work in Omaha.

That was followed by a tour of an insurance company, guided by its president. And it is there, in the Omaha area, that Whelan must do well, where Democratic successes must be great anough to offset Republican votes eslewhere in the state.

Thone, in fact, apparently has been able to lead Whelan statewide in polls so far by lagging only slightly in the area around Omaha.

For his part, Thone will tell an audience a long tired joke, and he sells himself as one who could work better with the nominally nonpartisan, but actually Republican legislature. "You can accomplish a lot more working with them," he said, "than with confrontation."

That would be a sharp contrast to Exon's government by veto - at least 155 of them in the past eight years, more vetoes than by any previous governor. Exon even once vetoed a bill the legislature passed to fund its own existence.