The Victorian-style apartment complex now under construction in the heart of old Georgetown would be a desirable residence for anyone in the District, but only Georgetown University students will be able to call it home.

The new four-story apartment house will be erected on a two-acre tract of open space at 37th Street NW between O and N Streets and across from Healy Hall as part of a two-pronged effort by Georgetown officials to respond to students' increased demand for on-campus housing.

"We've had a waiting list for housing a mile long," said Winifred M. Wegmann, director of residences at Georgetown. "Students are simply unable to find affordable housing in this area."

Georgetown is not alone. Spokesmen for colleges in the city said their schools also have waiting lists of students asking for more rooms than they can provide.

Some area colleges, like Georgetown, are investing capital into new dormitories. And others, already hampered by a lack of space on their urban campuses, are hoping the demand will ease as the number of college-age students decreases. All said they have been trying to cope with student housing demands for years.

American University spent $3.2 million last year to buy an old Baptist retirement home and turn it into housing for 100 students, said spokeswoman Marion Martin.

At George Washington University, Housing Director Ann E. Webster said the school once rented the several apartment houses it owns to the general public but has turned the buildings into student housing. She said the school is moving undergraduate students into two apartment houses formally reserved for graduate students. In 1976, the university bought the nearby Francis Scott Key hotel and turned it into a dormitory.

Howard University has no immediate plans to increase student housing but spokesman Alan Hermesch said the university has long-range plans to build dormitories on both the main and west campuses because of student demand.

Only D.C.'s Catholic University, with an enrollment of 2,920 undergraduate students, reported no shortage; approximately 1,600 students there live in university-owned housing.

Webster, who has worked in the GWU housing department for 17 years, said she has seen a demand for student housing swing from a low in the late 1960s to an all-time high in the late 1970s.

"It used to be very easy for students to find good, cheap apartments around here," she said. "But then the apartment houses all went condo and the economy slipped. They were clamboring to get back into the dorms."

Webster said Foggy Bottom, where GWU is situated, is a desirable neighborhood where rents have been driven up beyond the average student's reach.

The same goes for Georgetown University, which runs a shuttle bus service to Arlington, the only place many students can afford to live, Wegmann said.

"They want to live near campus; that's only natural," she said. "That's why we decided to invest in more living space."

She said the new dorm, which will house 360 students two to a room, will cost the university $7.5 million. The school has just renovated an old academic building at 35th and N Sts. NW into apartments for another 224 students at a cost of $7.1 million.

Wegmann said the university hopes to meet its student housing demand with these two new facilities. Currently, 3,120 undergraduate students, out of an enrollment of 5,500, live in campus housing.

But residence directors said student housing demand may have peaked.

"We're anticipating a smaller freshman class next year and plan to switch some undergraduate housing back to graduate," said Webster.

At American, Martin said a slump in the District housing market has eased student demands for university-owned housing.

"At one point, the demand was very great, which was the impetus for buying the new building," she said. "Since then, there seems to be more outside apartments to go around. A lot of home owners can't sell, so they're renting."

Students also may be finding that on-campus housing is not necessarily a lower-proced alternative to finding their own rooms off campus. Most area universities have hiked their rents from year to year.

At Georgetown, rooms cost students anywhere from $1,800 to $2,430 each for the nine-month academic year, and students must double up, which means the university is receiving rent of $1,080 a month for its more desirable two-bedroom apartments.

American University charges students $1,948 to $2,800 each for a nine-month year depending on the room. Philip Henry, director of housing, said slightly more than half of the 5,500 undergraduate students live on campus.

Over at Catholic University, students must pay anywhere from $1,620 to a whopping $4,340 for a room or apartment for nine months, which means that some students pay the university $428 a month in rent.

George Washington University rooms cost from $1,820 to $2,010 a person for double occupancy for nine months. Webster said 2,460 students out of an undergraduate enrollment of 4,500 live in university housing.

Howard charges students as little as $771 an academic year each for a room, and their highest rent is $1,498 for nine months. Hermesch said 3,679 of 8,000 undergraduate students live on campus.

"It is accepted that city schools charge more because real estate is so much more expensive," said Wegmann.