The isolated and underdeveloped northwestern region of Galicia, birthplace of the late dictator Generalissimo Francisco Franco, became the third Spanish area to gain self-government yesterday when voters endorsed a referendum on home rule provided for under the current democratic constitution.

But more than 70 percent of the region's eligible voters failed to cast ballots -- a level of nonvoting twice that of the Basques and the Catalans who last year voted on the same ambitious plan to replace the strict centralism of the previous Spanish dictatorship with a quasi-federal state structure.

Galicia, like the Basque country and Catalonia in the northeast, has a cultural and linguistic tradition distinct from the rest of Spain. It voted enthusiastically, with a 75 percent turnout, for home rule in 1936 shortly before the outbreak of the Spanish Civil War.

That short-lived experiment in autonomy was crushed, together with home rule for the Basque and Catalan governments, by the Francoist dictatorship that emerged from the war. Yesterday's referendum in Galicia was a bid by the government, with the backing of all major parties, to make historic reparation and breathe new life into its program of turning over power to the regions.

With a disappointing turnout of just 26 percent of Galicia's 2.1 million voters, national and local politicians began searching for scapegoats. Politicians alternately blamed an untimely electoral season, an out-of-date census and a lackluster referendum campaign for a nonvoting rate that far exceeded the Madrid administration's most pessimistic forecasts.

In October last year, the northern Basque country, where separatist terrorists continue to wage an undercover war against the government, and the strongly nationalist Catalonia area became the first regions to obtain home rule. The two, together with Galicia, are termed "historic nationalities" by the two-year-old constitution that replaced Francoism.

As a result, they need only a simple majority of those voting in a local referendum to achieve an autonomous status.Among the minority of Galicians who did cast a vote yesterday, 70 percent endorsed the referendum on home rule. w

In contrast to the industralized Basque and Catalan areas, Galcia is marked by subsistence farming, chronic underdevelopment and a tradition of migration to Latin America that has led it to be known as the "goodbye land." mThe Galician language is a mixture of Portuguese and Castilian Spanish, and the local inhabitants are of Celtic origin, distant cousins of the Scots and Irish.

Galicia is now entitled theoretically to wide-ranging powers of self-government and will be holding elections for a local parliament next summer on the pattern already established by Catalonia and the Basque country. There, autonomous governments and elected assemblies are currently negotiating the actual transfer of responsibilities when the Madrid administration.