Hispanic Americans, the fastest-growing ethnic minority in the United States, are slowly moving toward power in politics - but they have a long way to go.

"We have been called a sleeping giant," said Rita Elizondo Thomson, head of the Washington office of the National Association of Latino Elected and Appointed Officials. "The giant is not sleeping anymore."He is not quite awake either. Statistics indicate that Hispanic political representation is not proportionate to their numbers or to their influence on U.S. cultural and economic life.

By the association's count, 3,317 Hispanics hold public office today, twice as many as a decade ago but only a minute fraction - O.67 percent - of the 490,000 elected officials in the country. Black Americans have almost twice as many representatives as Hispanics.

There is no Hispanic in the Senate, only 11 in the House, and a sole Hispanic governor, Robert Martinez of Florida.

At a meeting of 200 Hispanic leaders in Washington last year, improving representation was identified as the top priority for a community which now numbers nearly 20 million.

Despite the weak Hispanic hold on political power, political analysts and demographers predict that sheer numbers will turn Hispanics into key political players in the near future.

The Hispanic population has a growth rate five times as high as the national average, partly through immigration, partly because of a pattern of large families, partly because Hispanics account for roughly 11 percent of all U.S. births but only 4 percent of all deaths.

The U.S. Census Bureau forecasts that Hispanics will account for around 15 percent of the population by the year 2,000. A decade after that, Hispanics are expected to overtake blacks as the largest minority group.

More than half of today's Hispanics live in California and Texas, the biggest and among the most hotly contested states in the November presidential elections. Political analysts said Hispanics in these two states could tip the balance.

Consequently, Hispanic voters were courted as never before. Vice President George Bush, the Republican candidate, frequently stressed that he has three half-Mexican grandchildren, from son Jeb and his Mexican wife Columba.

The Democrats' Michael Dukakis delighted in showing off his fluent Spanish at campaign rallies.

"We are no longer ignored," said Elizondo. "We are being taken seriously."