I've been running for 15 months," says Robert Livingston, newly elected to the U.S. House of Representatives. "I've never stopped."

With the same persistence that won him honors as a parish, state and federal prosecutor, the rangy, 34-year-old candidate stalked Louisiana's 1st Congressional District since last summer, when he was the lone Republican in the race to succeed retiring Rep. F. Edward Hebert (D-La.).

He lost last year to Richard A. Tonry. But for months after taking office, Tonry resigned amid allegations of vote fraud in his party's primary campaign, and the campaign started again. On Saturday, it was over, and Livingston became the third Republican congressman in the state's eight-member House delegatio, winning in a district Democrats held for 102 years.

Livingston, whose party has only 5.4 per cent of the district's 222,995 registered voters, received 49.6 per cent of the vote in the special election Saturday - the fifth balloting in a year to pick a successor to Hebert. With all but one of 327 precincts reported, Livingston won 54,250 votes, sate Rep. Ron Faucheux, 27, the Democratic nominee, got 40,880 (37.3 per cent), and Sanford (Sandy) Kransnoff, 42, who ran as an "Independent Democrat," received 14,267 (13 per cent).

Livingston scored his coup by running well among two dissimilar goups of voters: rich people and blue-collar workers. He won more than 70 per cent of the vote in well-to-do precincts along Lake Pontchartrain in his hom territory of Algiers, which is across the Mississippi River from New Orleans. These are predominantly white areas.

He also garnered 65 per cent of the vote in St. Tammany Parish (county), which is across Lake Pontchartrain from New Orleans and attracts people who build large homes and commute to New Orleans daily or retire there, Livingston campaign chairman Ted Nass referred to these voters as "natural Republicans."

The blue-collar workers are in St. Bernard Parish, just east of New Orleans. In the party primaries last June, the political machine in the parish turned out the vote fornative son Tonry. Tonry won 70 per cent of the vote in that parish but lost the overall primary to Faucheux.

Eigh days after the quit Congress last May, Tonry was charged with obstructing justice and violating campaign finance laws. He pleaded guilty to a lesser offense and was sentenced to a $10,000 fine and a year in prison.

This time St. Bernard Parish Sheriff John (Jack) Rowley, who heads the political organization, made to endoresment but gave unofficial suport to Livingston. The sheriff's brother, Bert Rowley, drove Livingston around the parish, Nass said, and on Saturday, Livingston took 49.6 per cent of the vote there.

Rowley did not endorse Faucheux for two reasons: Faucheux had run against Tonry and he had the backing in both races of the rival Perez machine, which controls neighboring Plaquemines Parish. The Livingston campaign made no effort in Plaquemines, said campaign manager Allen Martin. Faucheux won 73 per cent of that parish's vote Saturday - the only one in the district he carried. Livingston also won 47.4 per cent of the vote in the part of Orleans Parish that is in his district - the eastern part of the city and the area along the lakefront.

In the June Democratic primary, Tonry had relied heavily on black votes which are primarily in Orleans Parish. He won easily in those precincts, but the turnouts were relatively low - between 30 per cent and 40 per cent. Faucheux had the same problem Saturday.

Another factor that hurt Faucheux in the black community was the independent, Krasnoff, who appears to have played a spoilers role. His positions were more liberal than Faucheux's, and he received the backing of the AFL-CIO and two black political groups. Krasnoff ran second to Faucheux in many normally Democratic areas, siphoning off votes that might otherwise have gone to the Democratic nominee.

In electing Livingston, the 1st district's voters have piced a Republican who shares much of Ronald Reagan's philosophy. A Regan delegate to the Republican National Convention last year, Livingston echoed Reagan during his campaign, saying that Americans have been "overtaxed, overregulated and overcontrolled" by the federal government.

Throughout his long campaign, Livingston downplayed the fat-cat Republican stereotype. As a youth, he says, "I was a pipefitter's helper, a shipbuilder's helper, a wedler's helper, a sheet-metal worker, you name it, I was there."