In the five years since Hong Qui Nam and his wife fled South Vietnam with their daughter, they have learned to use credit cards, begun saving for a small suburban Washington house, and bought two cars -- small but important steps in their eyes toward becoming American.

But this year the Hongs say they will at last be able to take the most important step of all: apply for U.S. citizenship and become Americans in word as well as deed.

The Hongs are not alone in their desire to become Americans. By December of this year, as many as 60,000 of the 112,000 Indochinese refugees who came to the United States in 1975 are expected to have filed petitions for citizenship.

So huge are the numbers involved -- more petitions are expected to be filed in 1980 than at any time in the last 35 years -- that Immigration and Naturalization Service officials predict the time required to process applications may grow from as little as four months to as long as 1 1/2 years.

In the Washington area alone, which has the fourth-largest refugee population in the country, officials estimate that 3,000 of the 14,000 Indochinese here will file. That will double the normal annual filing load of 3,000 to 6,000.

"It's going to be a huge job," said Kellogg Whittick, director of the INS Washington District office. "We have a very large backlog already. We're going to need all the help we can get."

The reasons behind the rush to citizenship are simple, according to Al Velarde, a U.S. Catholic Conference official in El Paso, Tex., who works with Mexicans and Indochinese who want to become Americans.

"First, they can vote, and that means a lot to them since they've given up their homeland," Velarde said. "Then they can be employed by the federal, state, and local governments since a lot of jobs are restricted to American citizens.

"But probably most important to the Indochinese and Mexicans alike is that, as American citizens, they can get the rest of their families still in the home country into the United States a lot more quickly than if they weren't citizens."

If there were no other reason to naturalize, said Hong who wants most to see his largely Americanized daughter a citizen, that aspect along would make it necessary for him and his wife to become American citizens.

"I have three brothers and two sisters still in Vietnam," Hong, 41, said. "My youngest brother is still in a re-education camp [operated by the Communists to 're-educate' those they see as possible threats].He was a military officer in the old army. I want to get him into America as fast as I can."

As a result, the sheer numbers expected to file have prompted the INS and the voluntary agencies that have worked with the refugees to try to develop ways to speed up the citizenship process.

Since October, for instance, the INS has been meeting with voluntary agencies here and around the country to develop an emergency strategy to deal with the expected surge. Training sessions for agencies' staffs have been arranged so that those Indochinese who might qualify will be assured of receiving proper counseling and instruction.

In addition, efforts will be made by the agencies to assist the INS by pre-screening potential petitioners so that the applications of those who do not qualify are weeded out before they needlessly clog the bureaucracy.

There have also been discussions about holding mass naturalization ceremonies rather than the traditionally small ceremonies in courtrooms.

Because of the waiting time already faced by other immigrants petitioning for citizenship, said E. B. Duarte, director of the immigration service's community efforts, the program to help speed up the process for the Indochinese is open to all immigrants, including Mexicans, wanting to become citizens.

Even so, he said, Indochinese have an advantage over others. Thanks to congressional legislation passed during the height of the refugee influx, those Indochinese petitioning for citizenship will be entitled to go to the head of the citizenship waiting list if they can show that immediate family members are still in Indochina.

In order to qualify for citizenship, the applicant must have been a legal resident of the United States for five years, be of "good moral standing," have two witnesses who can testify to the applicant's character, and be able to pass simple English and American history and government tests.

Because of the unique makeup of the Indochinese population in the Washington area -- which has a high proportion of highly educated professionals -- officials say they anticipate that proportionately more of them here will apply for citizenship than anywhere else in the country.

Yet, not all of the 112,000 Indochinese who came to the United States in 1975 will qualify or even file petitions, said Vu K. Thu, a former South Vietnamese diplomat now working with the U.S. Catholic Conference in Washington.

"Some of them are too old," he said. "They live with their children and grandchildren and speak only Vietnamese at home. They have little contact with those outside the home, so they have not had the opportunity to learn enough English to pass simple tests. Others are children who do not need to file petitions because they will become Americans automatically when their parents become citizens. Some may have problems with their residency requirements. But most will want to apply some day."

Hong and his wife, Tran, former teachers, are among those locally who will apply. Since they arrived in June 1975, they have studied English at night school, speak English at home whenever they can, take corrections from their now fluent daughter Mimi, 12, and listen to English-language tapes and records that they check out from the library.

"I read the book about two presidents and the first ladies and I study geography -- where Maryland is located on the map, where is California," Hong said.

"Now I have credit cards, I pay the bills every month, and I read the newspaper every morning," Hong said. In Saigon, he said, everything was paid by cash and there were no credit cards. "My American friends warn me about credit cards. They say, 'Don't charge too much.' So I use them just for simple things and pay the bills off each month. I got a letter from Exxon telling me what a good customer I was!"

Meanwhile they speak proudly of their daughter's success in school, where she receives straight A's and her ability to find new friends and integrate into the culture. "They have teen clubs and softball and roller skating," Hong said.

But there are some aspects of American life that trouble them, too, he added. "The children have dancing," he began.

"And parties," interrupted his wife.

"We think she is too young for those things," he said, as his daughter smiled shyly.

All of this rapid success has been achieved at great personal cost. When they first came to the Washington area, Hong worked as a laundry boy for a hotel and his wife worked as a waitress in a restaurant. Meanwhile, he studied drafting at night -- completing a two-year course in 15 months -- while his wife studied typing and secretarial skills.

Now she works as a clerk-typist and he as a draftsman.

"Everyday the difference between Americans and us gets smaller and smaller," he said. "It is a very, very good way to live."