The Basque country and Catalonia voted heavily today to accept statutes restoring the autonomous regional governments that were suppressed in the 1930s by the dictatorship of Generalissimo Francisco Franco.

The voting gives home rule to 2.5 million Basques and 7 million Catalans, almost a third of Spain's 36 million people. The recreation of autonomous Basque and Catalan regions was considered the last, and toughest, major step in the restoration of Spanish democracy after almost 40 years of Franco's dictatorship.

This step had been heavily opposed by the armed forces, which viewed the lossening of centralized government as a threat to national unity. Other highly centralized European governments were also anxious about the change. This is especially true of neighboring France, which has small Basque and Catalan minorities of its own along the border it shares with Spain as well as growing separatist movements in Brittany, Corsica and elsewhere.

Failure to grant autonomy to the Basques more rapidly led to the continuation after Franco's death and growth of anti-Spanish terrorism that cost the lives of dozens of Spanish police and a large number of high-ranking Army officers throughout the country.

Only yesterday, a 90-yard tunnel was discovered leading under an apartment building occupied by Spanish officers and their families in the Catalan capital of Barcelona. The civil governor there said that discovery of the tunnel, estimated to have taken seven months to dig by hand, had averted a "a holocaust" if the building had been blown up.

The Catalan result, with 88 percent approval of the new statutes in the metropolis of Barcelona, had been expected. But the turnout of more than 60 percent of voters in the Basque country had been a question mark. The Basque terrorist organization ETA had campaigned for a boycott of the referendum. Ninety percent of those who voted were expected to cast yes ballots.

In one of the three Basque administrative provinces that voted today, 63 percent of the electorate showed up and 93 percent of them voted yes, with almost half the vote counted.

By contrast, in the Spanish national constitutional referendum last year 43.5 percent of the voters turned out in the Basque country's two main provinces. That referendum also was boycotted by the dominant Basque National Party.

The Basque National Party, which negotiated the autonomy statute with Spanish Premier Adolfo Suarez this summer, pulled out all the stops to get out the vote. It hired an advertising agency to produce sophiscated posters, newspaper ads and radio spots depicting a cross section of ordinary Basques saying they were going to vote yes.

The Basque National Party's well-established electoral machinery -- based on an apparatus created in 1903 as an independence party cutting across class and social lines -- is expected to help sweep it to power in the new Basque parliament. The elections should be held in February or March.

The party is also helped by its historic ties with the Catholic Church. The church made clear that it favored the autonomy statute by declaring that people should get out and vote. Given the ETA boycott campaign, the church's call could only mean vote yes.

Now the Basque National Party -- an underground opposition party for all but the year it held power before Franco swept away the short-lived Basque republican government in 1937 -- must learn to govern.

Although there are still many major problems on which the new Basque government could stumble badly, it is assumed widely that passage of the autonomy statute means that the Basque country has avoided turning itself into a Spanish Ulster.

But much mutual distrust between the Basques and the Madrid government is still to be overcome. Many Spaniards, especially in the armed forces, suspect that the Basques are going to use the autonomy statute as a steppingstone to total independence. Many Basques suspect that the Spanish government will try to gut the autonomy statute of any real meaning by interpreting it in the narrowest possible way.

Government spokesman have already said that creation of a native Basque police force does not mean that the national police will leave the Basque country.

The most universal complaint of the Basques is the presence here of about 12,000 policemen from other regions of Spain, who are perceived as an occupying army. They were out in full force today at polling places and frequent roadblocks on the highways, patrolling in large numbers with rifles and submachine guns.

The representative in Bilbao of a major Western country said that foreign visitiors here expect him to tell them that the people are sick of terrorism. Instead, he must disabuse them of that idea by saying that it is the police that they are sick of.

"Invariably," he said, "at almost any political meeting you go to, no matter how moderate the party, one of the first questions from the audience is, 'when are they going to leave?' "

Unlike the Catalans, the Basques won a major political weapon in their autonomy negotiations -- the power of the purse string. The new Basque regional government will collect all taxes and then negotiate with Madrid about what portion goes to the central government. This could give the Basque government the leverage to insure a generous interpretation of the statute by Madrid.

There is new hope that Basque terrorism could die down quickly. A spokesman for the ETA terrorist organization admitted yesterday that his group had been observing a truce for the past twelve days. He said that, while the referendum vote was held under Franco-style conditions, "if the Basque people demonstrate that they do not want the armed struggle to continue, we will abandon it."