WASHINGTON (AP) _ The dismal showing by disciples of political extremist Lyndon LaRouche in Tuesday's primaries proves that LaRouche victories in Illinois in March were a fluke, a Democratic official said Wednesday.

''They zeroed out,'' Democratic National Committee spokesman Terry Michael said of contested primary races in Indiana, North Carolina and Ohio.

The only nominations won by LaRouche candidates were by default - no other Democrats filed - in two congressional districts in Ohio and another two in the Texas primary on Saturday.

''The results of these first primaries make it clear that the Illinois nomination of two LaRouche cult members was indeed a fluke, that as long as the party and news media do a reasonably good job of educating voters about who these people are, they will be rejected out of hand. That's what happened,'' Michael said.

LaRouche spokesman Mel Klenetsky said that while the results Tuesday ''were not as dramatic as Illinois they nevertheless continue the same pattern. Our influence is growing.'' He said LaRouche candidates, while not winning any nominations outright, drew significant blue-collar and rural votes.

He also said the campaign was investigating the possibility of vote fraud, a favorite LaRouche defense, in Indiana and Ohio. He would not go into detail, other than to say ''electrical blackouts caused computers to go down. Patterns that were favorable to us prior to the blackout suddenly started going in the opposite direction.''

Storms swept the Upper Midwest on Tuesday night. In Ohio, a storm shorted out computers and delayed vote counting in two counties. In Indiana, scattered power outages were reported through the night.

LaRouche, a perennial presidential candidate, was swamped with media attention after the March 18 Illinois primary when two followers won the nominations for lieutenant governor and secretary of state, knocking off candidates hand-picked by the Democrats. Those victories also brought to the fore LaRouche's unconventional beliefs, among them that the Queen of England backs an international drug ring and that AIDS victims should be quarantined.

The race this week that most concerned Democrats was the Indiana U.S. Senate primary, where Jill L. Long, a largely unknown university professor endorsed by the state party, faced Georgia Irey, a LaRouche follower who had top billing on the ballot.

Long captured 74 percent of the vote on Tuesday and will face Sen. Dan Quayle in November.

Irey said she was not disappointed because ''we're building a constituency here'' and she hinted at a possible challenge to Sen. Richard Lugar in 1988.

''I've had a wonderful time,'' she said. ''It's really fun to express what I've been yelling at the television set for such a long time. Now I can say it in public and people will listen to me.''

In Ohio, LaRouche candidate Don Scott got 13 percent against Sen. John Glenn in the Democratic primary.

Twelve LaRouche supporters in contested congressional races lost in Ohio; however, two who were unopposed - Clem Cratty in the 4th District and Donald Jones in the 6th District - will face Republican incumbents in the November election.

Michael said it was up to state and local party officials to decide how to handle those races where LaRouche candidates by default wound up being the party standardbearer.

''At this point, it seems almost outside the realm of any possibility that they could go on to win public office in November. That is the most important consideration,'' he said.

In North Carolina, a U.S. Senate candidate with ties to LaRouche, Milton Croom, finished ninth in a 10-way primary won by former Gov. Terry Sanford.

The only LaRouche candidate who came close to winning was Donald Varella, running for the Democratic chairmanship in San Antonio. He won 39 percent of the vote in Saturday's primary and must face an establishment candidate in a runoff.

''Anyone who would call Varella's victory a fluke is an idiot. It's clear there are a lot of people interested in what we're saying,'' said Harley Schlanger, Southwest chairman for LaRouche's National Democratic Policy Committee.