Conditions at the single building that makes up the Alexandria campus of the Northern Virginia Community College are so crowded that the schools 160 full-time professors must share a corner of the library for their "offices."

Since the modern, four-story building opened in 1973, the student population has doubled to 10,000 and many classes are now conducted in area high schools and even in some firehouses and local court rooms.

The popularity of the little known school - tucked in among the high-rises of western Alexandria - has made the Alexandria branch of the NVCC one of the fastest growing institutions in the country.

As a result, voters last fall approved an expansion program for the college that will help it seat the students it already has. Gov. John N. Dalton yesterday awarded a contract for a $4.3 million classroom and administration building.

The school ascribes its success to two ingredients: low tuition and wide course offerings that include classes in liberal arts, law enforcement, and occupational health and safety, among others.

"It's not a drop-out institution," said Jean Netherton, who has been the provost of the Alexandria campus for two years. The average student is 28 years old and about 80 percent of the student body is employed. "A great many of them are upgrading job skills," she added.

A striking characteristic of the student body is the large number of foreign students enrolled, about 10 percent of the schools's population. Of these, nearly one-third ar from Southeast Asia, mainly war refugees from Vietnam and Cambodia.

Two Vietnamese students who fled during the fall of Saigon in 1975 said they were attracted to the school because the professors at the school appeared to "understand the problems of the Vietnamese." Both women refused to give their names to a reporter, but when asked why they attended the college, one of them replied:

"Because the Vietnamese have been struggling all their life, so this is just a new struggle to get into a new society."

For many students, the low tuition costs are a major factor in their decision to attend Northern Virginia Community College, which has four campuses in addition to the one in Alexandria. For Virginia residents, the charge is $8.50 per credit hour, and a three-credit course costs $25.50.

Professors interviewed at random agreed that the student body is is highly motivated. "You're not getting freshmen whose father and mother are saying, 'You go to college,'" remarked one counselor.

Chih-mei Chen, a psychology professor, said many students are interested in pursuing their education at the traditional four-year colleges after they earn their associate degree.

"We have two extremes," Chen said of the student body. "Some are very good and others are really ill-prepared, with few in the middle."

The only requirements for admission to the NVCC system are that students be high school graduates or 18 years old. John Popeck, the dean of students, said about 10 percent of the students have not graduated from high school.

The money approved by the governor yesterday is part of an $86.5 million bond issue approved by Virginia voters last November. The new building at the Alexandria campus will include classroom and administrative offices and will be attached to the existing structure.

A separate building to house the school's mechanic school is also planned. Many of the courses in automotive maintenance are now held in a warehouse at Bailtey's Crossroads, the same one where in 1965 the NVCC system was born with 500 students.