All Spanish nationals who reside in the United States are subject to American legislation, with the exception of those individuals in the diplomatic corps. As foreign residents, Spaniards living in the U.S. are also subject to the immigration and naturalization laws.
In addition to American legistation, three Spanish laws are of special interest to Spanish nationals in the U.S.:
Statue on Spanish Nationals Abroad
The Statute on Spanish nationals abroad was approved December 14, 2006 and entered into force two days later.
It constitutes the legal framework to guarantee to all Spaniards abroad their constitutional rights, and to tighten social, cultural, economic and linguistic ties to Spain and their regions of origin.
The bill establishes the basic actions by the Spanish central government and its Autonomous Comunities in order to improve the well-being of Spanish nationals abroad in those areas where the assistance in the country of residence should be complemented.
Finally, the law lists specific measures by the Spanish central government and the Autonomous Communities to improve services to Spanish citizens abroad, such as social and work integration to those who decide to return to Spain.
Read the new statute on Spanish nationals abroad (requires Adobe Acobat Reader) here: 
Spanish Citizenship Law
The new law on citizenship was approved October 8, 2002 and entered into force January 9, 2003. It was approved by the government presided by José María Aznar, of the People's Party of Spain. The law realizes a series of long-sought aspirations of Spanish citizens living and working abroad. In particualr, it recognizes the right of indivuduals to keep and re-gain Spanish citizensip when they become naturalized citizens of other countries. In summary:
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If a Spanish national who resides abroad acquires voluntarily the citizenship of the country he resides in, he can keep his Spanish citizenship, provided he declares that he wishes to do so at the
Spanish Consulate closest to his residence within 3 years of acquiring his new citizenship. A declaration is not required for citizens of Ibero-American countries, Andorra, the Philipines, Equatorial Guinea and Portugal.
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If a person born in Spain or born in a foreign country to a Spanish citizen loses his Spanish citizenship in a foreign country, he can get it back at the Spanish Consulate closest to his residence without having to renounce to his current citizenship.
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Any person whose natural father or mother is or has been a Spanish citizen born in Spain can apply for Spanish citizenship, provided he renounces to his current citizenship. Citizens of Ibero-American countries, Andorra, the Philipines, Equatorial Guinea and Portugal are exempt from the last requirement.
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A Spanish citizen born in a foreign country to parents also born abroad needs to declare that he wishes to keep his Spanish citizenship at the Spanish Consulate closest to his residence within three years of turning 18.
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Any person with at least one grandfather or grandmother born in Spain can apply for Spanish citizenship after one year of legal residence in Spain.
Read the new Spanish law of citizenship here:
Agreement on Social Security
On September 30, 1986 the governments of Spain and the United States signed an agreement on Social Security and an administrative arrangement for its implementation. Both bills entered into force April 1, 1988; they regulate the mutual recognition of Social Security benefits in favor of individuals subject to the legislation of one or both countries, and spell out the requirements that guide the application of the legislation of either Spain or the United States.
Read the agreement on Social Security between Spain and the United States here:
