Roberto de la Madrid, a once poor bilingual son of migrant workers who made it big in banking, oil and politics, today became the first American-born governor of a Mexican state Baja California.

De la Madrid's inauguration for a six-year term was hailed by Mexican President Jose Lopez Portillo and California Gov. Edmund G. (Jerry) Brown Jr. as ushering in a new era of friendly border relations between Baja California and California.

It is widely believed here and in San Diego that De la Madrid's close ties with business and political communities on both sides of the borader can help in solving troublesome problems of illegal immigration, drug traffic and tourist safety that have strained U.S.-Mexican relations during the past decade.

De la Madrid believes that the key to solving these problems is economic development to provide jobs in Baja California, where unemployment is now estimated at 22 per cent.

"Roberto do you best so that Mexicans who come here can find work - so that they do not cross the border to the United States," Lopez Portillo said to loud applause.

Among those attending the festive ceremony in this border town were Brown and San Diego mayor Peter Wilson, one of several Republican challengers for the California governorship. Brown said that California had a keen interest in development of oil and gas reserves in Baja California.

"We're going to have a very close relationship," Brown added."I see the two states as inextricably linked. I see that not as a problem but as an oppotunity."

Wilson and De la Madrid, who once served as chairman of the San Diego Planning Commission, are old friends. Another old friend who attended the inaugural ceremony was actor John Wayne, who met De la Madrid when the latter was doing bit parts in movies as a horseman.

De la Madrid, 55, was born in Calexico, Calif. across the border from Mexicali but his parents brought him here soon after birth and registered him as a Mexican citizen. He started in the banking business and then founded a petroleum company that distributed products for U.S. oil companies and Pemex, the state owned Mexican oil Monopoly.

Personal ties are the key to doing business in Mexico, and De la Madrid has many friends on both sides of the border. His most important friend is Lopez Portillo, who used to ride and hike with De la Madrid and talk about Mexico's future.

In Mexico, there is frequently subtle prejudice against Mexicans who are born in the United States, but De la Madrid's warm, out-going personality and his American-style campaign techniques that stress his humble origins appear to have overcome this handicap. His campaign poster said simply, "Roberto."

It was not the posters but Lopez Portillo who made De la Madrid governor of Baja. The new governor was opposed by conservatives in his bid for nomination by the dominant Party of the Institutional Revolution (PRI), but the conservative candidate died during the election campaign. Lopez Portillo immediately designated De la Madrid as the replacement.

Even though Baja is one of the few Mexican states where the ruling PRI has been seriously challenged. De la Madrid was elected Aug. 7 by a 2-1 majority. He has since met with Brown. Wilson and other California officials and pledged his cooperation in mutual affairs.

In his inaugural speech, De la Madrid talked about economic development and self-reliance as the path to a better life for Mexico.

He called for more development along the border of manufacturing plants that assemble component parts for U.S. companies with a largely Mexican labor force. He also promised to create "the best possible incentives" for investment and said that it is necessary for Mexican products to find a market in California.

Later, at a joint press conference for American reporters with Brown. De la Madrid said, "We need investment to industrialize so that we can export finished products rather than new material or human beings."

He also reaffirmed his support for legalized gambling in Baja California, a proposal that would need approval from the Mexican Congress before it could go into effect. Brown said there would be "a lot of takers from California" if Baja were able to legalize gambling.

In his inaugural address, De la Madrid also promised to create a bureau that would be specifically changed with defending the rights of tourists in Mexico, a step viewed by both American and Mexican businessmen as a necessary assurance for the tourist trade.

The warm, harmonious atmosphere today demonstrated the close ties between the United States and Mexico that have been forged by Lopez Portillo and President Carter. It also reminded those attending the ceremony of an old saying that Lopez Portillo quoted when he visited Washington in February.